Education  Library 


A  SYSTEM 


OF 


NATURAL   PHILOSOPHY 


IN  WHICH  THE 

PRINCIPLES  OF  MECHANICS, 

HYDROSTATICS,    HYDRAULICS,    PNEUMATICS,    ACOUSTICS,    OPTICS, 

ASTRONOMY,  ELECTRICITY,  MAGNETISM,  STEAM  ENGINE, 

AND  ELECTRO-MAGNETISM, 

ARE 

FAMILI  ARLY     EXPLAINED, 

AND  ILLUSTRATED  BY 

MORE  THAN  TWO  HUNDRED  ENGRAVINGS. 

TO  WHICH  ARE  ADDED, 

aUESTlONS  FOR  THE  EXAMINATION  OF  PUPILS. 

DESIGNED  FOR 
THE  USE  OF  SCHOOLS  AND  ACADEMIES. 

BY  J,  L  eOMSTOCK,  M,  D, 

Author  of  Introduction  to  Mineralogy,  Elements  of  Chemistry,  Introduction  to 
Botany,  Outlines  of  Geology,  Outlines  of  Physiology,  Nat.  Hist.  Birds.  &c. 


STEREOTYPED  FROM  THE  FIFTY-THIRD  EDITION. 


NEW-YORK: 

ROBINSON,    PRATT,    &   CO. 

63   WALL-STREET. 

1840. 


ENTERED,    ^ 
According  to  act  of  Congress,  in  the  year  183S,  by 

J.  L.  COMSTOCK, 
in  the  Clerk's  Office  of  the  District  Court  of  Connec.,-  r 


•'  v 

JJ./. 


ADVERTISEMENT 

THE  necessity  of  reprinting  the  Author's  Natural 
Philosophy,  has  given  him  an  opportunity  of  reviewing 
and  correcting  the  whole,  and  of  making  many  changes, 
which  could  not  have  been  done  on  stereotype  plates. 
In  addition  to  these  corrections,  he  has  added  about 
forty  pages  of  letterpress,  and  more  than  twenty  new 
cuts,  chiefly  on  the  subjects  of  the  Steam  Engine  and 
Electro- Magnetism.  Both  these  subjects  the  Author 
has  taken  £reat  pains  to  explain  and  illustrate,  in 
such  a  manner  as  to  make  them  understood  by  the 
pupil.  The  mechanical  principles  on  which  this 
engine  acts,  it  will  be  allowed,  have  been  comprehend- 
ed only  by  a  very  few  ;  while  the  subject  of  electro- 
magnetism  has  become  exceedingly  interesting,  on 
account  of  recent  attempts  to  make  its  force  a  motive 
power.  The  whole  work  has  been  newly  stereotyped ; 
and  on  all  accounts,  therefore,  it  is  believed,  will  be 
much  more  acceptable  to  the  public  than  formerly. 

J.  L.  C. 

Hartford,  Ct.,  May,  1838. 


QCQiV 


PREFACE. 


WHILE  we  have  recent  and  improved  systems  of  Geogra- 
phy, of  Arithmetic,  and  of  Grammar,  in  ample  variety,  —  and 
Reading  and  Spelling  Books  in  corresponding  abundance, 
many  of  which  show  our  advancement  in  the  science  of  edu- 
cation, no  one  has  offered  to  the  public,  for  the  use  of  our 
schools,  any  new  or  improved  system  of  Natural  Philosophy. 
And  yet  this  is  a  branch  of  education  very  extensively  studied 
at  the  present  time,  and  probably  would  be  much  more  so, 
were  some  of  its  parts  so  explained  and  illustrated  as  to  make 
them  more  easily  understood. 

The  author  therefore  undertook  the  following  work  at  the 
suggestion  of  several  eminent  teachers,  who  for  years  have 
regretted  the  want  of  a  book  on  this  subject,  more  familiar 
in  its  explanations,  and  more  ample  in  its  details,  than  any 
now  in  common  use. 

The  Conversations  on  Natural  Philosophy,  a  foreign  work 
now  extensively  used  in  schools,  though  beautifully  written, 
and  often  highly  interesting,  is,  on  the  whole,  considered  by 
most  instructors  as  exceedingly  deficient  —  particularly  in 
wanting  such  a  method  in  its  explanations,  as  to  convey  to 
the  mind  of  the  pupil  precise  and  definite  ideas  ;  and  also  in 
the  omission  of  many  subjects,  in  themselves  most  useful  to 
the  student,  and  at  the  same  time  most  easily  taught. 

It  is  also  doubted  by  many  instructors,  whether  Conversa- 
tions is  the  best  form  for  a  book  of  instruction,  and  particu  - 
larly  on  the  several  subjects  embraced  in  a  system  of  Natu- 
ral Philosophy.  Indeed,  those  who  have  had  most  experi- 
ence as  teachers,  are  decidedly  of  the  opinion  that  it  is  not; 
and  hence,  we  learn,  that  m  those  parts  of  Europe  where  the 
subject  of  education  has  received  the  most  attention,  and, 
consequently,  where  the  best  methods  of  conveying  instruc- 
tion are  supposed  to  have  been  adopted,  school  books,  in  the 
form  of  conversations,  are  at  present  entirely  out  of  use. 

1* 


INDEX. 


J. 

Juno,  241. 
Jupiter,  242. 

Perkins'  experiments,  95 
Prismatic  spectrum,  219. 
Properties  of  bodies,  9. 

Pneumatics,  124. 

L. 

Pumps,  139. 

Latitude  and  Longitude,  294. 

common,  140. 

how  found,  296. 

forcing,  141. 

Leyden  jar,  313. 

Pulley,  82. 

Lenses,  various  kinds  of  194. 

/  *  . 

Lever,  66. 

R. 

compound,  73. 

Rainbow,  221. 

Level,  water,  101-108 

Rarity,  21. 

Lightning-rods,  310. 

Rockets,  how  moved,  40. 

Light,  refraction  of  i72. 

Reflection  by  lenses,  193. 

reflection  jf,  175. 

Longitude,  294. 

S. 

how  found,  297. 

Seasons,  260. 

heat  and  cold  of,  2(55 

M. 

Screw,  89. 

Magic  lantern,  217. 
Magnetism,  316. 

perpetual,  92. 
Archimedes',  119. 

electro,  324. 
Matter,  inertia  of,  13. 
Malleability,  23. 

Sound,  propagation  of,  161 
reflection  of,  163. 
Spring,  intermitting,  112. 

Mars,  240. 

Solar  system,  228. 

Magnetic  needle,  319. 

Steelyards,  70. 

Magnets,  revolution  of,  332. 

Solar  and  siderial  time,  271  . 

Mechanics,  64. 

Stars,  fixed,  299. 

Metronome,  63. 

Steam-engine,  144. 

Mercury,  238. 

Savary's,  144. 

Microscope,  208. 

Newcomen's,  147. 

solar,  209.  . 

Watt's,  151. 

compound,  211. 

low  and  high  presstuio   l!ff 

Momentum,  38. 

Sun,  235. 

Mechanical  powers,  92. 

Syphon,  111. 

Mirrors,  176. 

convex,  179. 

T. 

concave,  186. 

Telescope,  211. 

metallic,  192. 

reflecting,  214. 

Moon,  240. 

refracting,  211. 

time  of  falling  to  the  earth,  31. 

Tides,  292. 

phases  of,  284. 

surface  of,  2S6.  ' 

U. 

Motion  denned,  36. 

Uniting  wire,  what,  326. 

absolute  and  relative,  37. 

velocity  of,  37. 

V. 

reflected,  40. 

Velocity  of  falling  bodies,  31. 

compound,  43. 

Venus,  238. 

circular,  43. 

Vision,  199. 

crank,  155. 

perfect,  202. 

curvilinear,  53. 

imperfect,  202. 

resultant,  58. 

angle  of,  203. 

Musical  strings,  165. 

Vesta,  241. 

instruments,  164. 

Volta's  pile,  323. 

Musk,  scent  of,  11. 

W. 

0. 

Optics,  169. 

Wedge,  88. 
Windlass,  76. 

definitions  in,  170. 
Optical  instruments,  208. 
Orbit,  what,  230. 

Water,  elasticity  of,  95. 
equal  pressure  of,  96. 
bursting  power  of,  100. 

P. 

raised  by  ropes,  122. 
Wood,  composition  of,  12. 

Pallas,  241. 
Planets,  density  of,  234. 
situation  of,  247. 

Whispering  gallery,  164. 
Wind,  166. 
trade,  168. 

motions  of,  248. 

Pendulum,  60. 

Z.           „    ' 

Penumbra,  29L 

Zodiac,  232. 

NATURAL     PHILOSOPHY. 


THE  PROPERTIES  OF  BODIES. 

1.  A  BODY  is  any  substance  of  which  we  can  gain  a 
knowledge  by  our  senses.     Hence  air,  water,  and  earth, 
in  all  their  modifications,  are  called  bodies. 

2.  There  are  certain  properties  which  are  common  to  all 
bodies.     These  are  called  the  essential  properties  of  bodies. 
They  are  Impenetrability,  Extension,  Figure,  Divisibility, 
Inertia,  and  Attraction. 

3.  IMPENETRABILITY. — By  impenetrability,  it  is  meant 
that  two  bodies  cannot  occupy  the  same  space  at  the  same 
time,  or,  that  the  ultimate  particles  of  matter  cannot  be  pene- 
trated.    Thus,  if  a  vessel  be  exactly  filled  with  water,  and  a 
stone,  or  any  other  substance  heavier  than  water,  be  dropped 
into  it,  a  quantity  of  water  will  overflow,  just  equal  to  the 
size  of  the  heavy  body.     This  shows  that  the  stone  only 
separates  or  displaces  the  particles  of  water,  and  therefore 
that  the  two  substances  cannot  exist  in  the  same  place  at  the 
same  time.     If  a  glass  tube  open  at  the  bottom,  and  closed 
with  the  thumb  at  the  top,  be  pressed  down  into  a  vessel  of 
water,  the  liquid  will  not  rise  up  and  fill  the  tube,  because 
the  air  already  in  the  tube  resists  it ;  but  if  the  thumb  be  re- 
moved, so  that  the  air  can  pass  out,  the  water  will  instantly 
rise  as  high  on  the  inside  of  the  tube  as  it  is  on  the  outside. 
This  shows  that  the  air  is  impenetrable  to  the  water. 

4.  If  a  nail  be  driven  into  a  board,  in  common  language,  it 
is  said  to  penetrate  the  wood,  but  in  the  language  of  philoso- 
phy it  only  separates,  or  displaces  the  particles  of  the  wood. 

What  is  a  body  7  Mention  several  bodies.  What  are  the  essential 
properties  of  bodies'?  What  is  meant  by  impenetrability  ?  How  is  it 
proved  that  air  and  water  are  impenetrable  1  When  a  nail  is  driven 
into  a  board  or  piece  of  lead,  are  the  particles  of  these  bodies  penetrated 
or  separated  ? 


10  PROPERTIES  OF  BODIES. 

The  same  is  the  case,  if  the  nail  be  driven  into  a  piece  of 
lead ;  the  particles  of  the  lead  are  separated  from  each  other, 
and  crowded  together,  to  make  room  for  the  harder  body, 
but  the  particles  themselves  are  by  no  means  penetrated  by 
the  nail. 

5.  When  a  piece  of  gold  is  dissolved  in  an  acid,  the  par- 
ticles of  the  metal  are  divided,  or  separated  from  each  other, 
and  diffused  in  the  fluid,  but  the  particles  of  gold  are  suppo- 
sed still  to  be  entire,  for  if  the  acid  be  removed,  we  obtain 
the  gold  again  in  its  solid  form,  just  as  though  its  particles 
had  never  been  separated. 

6.  EXTENSION. — Every  body,  however  small,  must  have 
length,  breadth,  and  thickness,  since  no  substance  can  exist 
without  them.     By  extension,  therefore,  is  only  meant  these 
qualities.     Extension  has  no  respect  to  the  size,  or  shape  of 
a  body.     The  size  and  shape  of  a  block  of  wood  a  foot 
square  is  quite  different  from  that  of  a  walking  stick.     But 
they  both  equally  possess  length,  breadth,  and  thickness,  since 
the  stick  might  be  cut  into  little  blocks,  exactly  resembling 
in  shape  the  large  one.     And  these  little  cubes  might  again 
be  divided  until  they  were  only  the  hundredth  part  of  an  inch 
in  diameter,  and  still  it  is  obvious,  that  they  would  possess 
length,  breadth,  and  thickness,  for  they  could  yet  be  seen, 
felt,  and  measured.     But  suppose  each  of  these  little  blocks 
to  be  again  divided  a  thousand  times,  it  is  true  we  could  not 
measure  them,  but  still  they  would  possess  the  quality  of  ex- 
tension, as  really  as  they  did  before  division,  the  only  differ- 
ence being  in  respect  to  dimensions. 

7.  FIGURE,  or  form,  is  the  result  of  extension,  for  we  can- 
not conceive  that  a  body  has  length  and  breadth,  without  its 
also  having  some  kind  of  figure,  however  irregular. 

8.  Some  solid  bodies  have  certain  or  determinate  forms 
which  are  produced  by  nature,  and  are  always  the  same 
wherever  they  are  found.     Thus,  a  crystal  of  quartz  has  six 
sides,  while  a  garnet  has  twelve  sides,  these  numbers  being 
invariable.     Some  solids  are  so  irregular,  that  they  cannot 
be  compared  with  any  mathematical  figure.     This  is  the 
case  with  the  fragments  of  a  broken  rock,  chips  of  wood, 
fractured  glass,  &c. 

Are  the  particles  of  gold  dissolved,  or  only  separated,  by  the  acid  ? 
What  is  meant  by  extension  1  In  how  many  directions  do  bodies  pos- 
sess extension  1  Of  what  is  figure,  or  form,  the  result  1  Do  all  bodies 
possess  figure  ?  What  solids  are  regular  in  their  forms  1  What  bo- 
dies are  irregular  1 


PROPERTIES  OF  BODIES.  11 

9.  Fluid  bodies  have  no  determinate  forms,  but  take  their 

shapes  from  the  vessels  in  which  they  happen  to  be  placed. 

10.    DIVISIBILITY. — By  the  divisibility  of  matter,   we 

mean  that  a  body  may  be  divided  into  parts,  and  that  these 

parts  may  again  be  divided  into  other  parts. 

11.  It  is  quite  obvious,  that  if  we  break  a  piece  of  marble 
into  two  parts,  these  two  parts  may  again  be  divided,  and 
that  the  process  of  division  may  be  continued  until  these 
parts  are  so  small  as  not  individually  to  be  seen  or  felt. 
But  as  every  body,  however  small,  must  possess  extension 
and  form,  so  we  can  conceive  of  none  so  minute  but  that  it  may 
again  be  divided.  There  is,  however,  possibly  a  limit,  beyond 
which  bodies  cannot  be  actually  divided,  for  there  may  be 
reason  to  believe  that  the  atoms  of  matter  are  inidvisible 
by  any  means  in  our  power.     But  under  what  circumstances 
this  takes  place,  or  whether  it  is  in  the  power  of  man  during 
his  whole  life,  to  pulverize  any  substance  so  finely,  that  it 
may  not  again  be  broken,  is  unknown. 

12.  We  can  conceive,  in  some  degree,  how  minute  must 
be  the  particles  of  matter  from  circumstances  that  every  day 
come  within  our  knowledge. 

13.  A  single  grain  of  musk  will  scent  a  room  for  years, 
and  still  lose  no  appreciable  part  of  its  weight.     Here,  the 
particles  of  musk  must  be  floating  in  the  air  of  every  part 
of  the  room,  otherwise  they  could  not  be  every  where  per- 
ceived. 

14.  Gold  is  hammered  so  thin,  as  to  take  282,000  leaves 
to  make  an  inch  in  thickness.     Here,  the  particles  still  ad- 
here to  each  other,  notwithstanding  the  great  surface  which 
they  cover, — a  single  grain  being  sufficient  to  extend  over  a 
surface  of  fifty  square  inches. 

1 5.  The  ultimate  particles  of  matter,  however  widely  they 
may  be  diffused,  are  not  individually  destroyed,  or  lost,  but 
under  certain  circumstances,  may  again  be  collected  into  a 
body  without  change  of  form.     Mercury,  water,  and  many 
other  substances,  may  be  converted  into  vapor,  or  distilled  in 
close  vessels,  without  any  of  their  particles  being  lost.     In 


What  is  meant  by  divisibility  of  matter  7  Is  there  any  limit  to  the 
divisibility  of  matter  1  Are  the  atoms  of  matter  divisible  1  What  ex- 
amples are  given  of  the  divisibility  of  matter  1  How  many  leaves  of 
gold  does  it  take  to  make  an  inch  in  thickness  1  How  many  square 
inches  may  a  grain  of  gold  be  made  to  cover"?  Under  what  circum- 
stances may  the  particles  of  matter  again  be  collected  in  their  original 
form  1 


12  PROPERTIES  OF  BODIES. 

such  cases,  there  is  no  decomposition  of  the  substances,  but 
only  a  change  of  form  by  the  heat,  and  hence  the  mercury 
and  water  assume  their  original  state  again  on  cooling. 

16.  When  bodies  suffer  decomposition  or  decay,  their  el- 
ementary particles,  in  like  manner,  are  neither  destroyed 
nor  lost,  but  only  enter  into  new  arrangements  or  combina- 
tions with  other  bodies. 

17.  When  a  piece  of  wood  is  heated  in  a  close  vessel,  such 
as  a  retort,  we  obtain  water,  an  acid,  several  kinds  of  gas.  and 
there  remains  a  black,  porous  substance,  called  charcoal. 
The  wood  is  thus  decomposed,  or  destroyed,  and  its  particles 
take  a  new  arrangement,  and  assume  new  forms,  but  that 
nothing  is  lost  is  proved  by  the  fact,  that  if  the  water,  acid, 
gasses,  and  charcoal,  be  collected  and  weighed,  they  will 
be  found  exactly  as  heavy  as  the  wood  was,  before  distillation. 

18.  Bones,   flesh,  or  any  animal  substance,  may  in  the 
same  manner  be  made  to  assume  new  forms,  without  losing 
a  particle  of  the  matter  which  they  originally  contained. 

19.  The  decay  of  animal  or  vegetable  bodies  in  the  open 
air,  or  in  the  ground,  is  only  a  process  by  which  the  particles 
of  which  they  were  composed,  change  their  places,  and  as- 
sume new  forms. 

20.  The  decay  and  decomposition  of  animals  and  vegeta- 
bles on  the  surface  of  the  earth  form  the  soil,  which  nou- 
rishes the  growth  of  plants  and  other  vegetables ;  arid  these, 
in  their  turn,  form  the  nutriment  of  animals.     Thus  is  there 
a  perpetual  change  from  death  to  life,  and  from  life  to  death, 
and  as  constant  a  succession  in  the  forms  and  places,  which 
the  particles  of  matter  assume.     Nothing  is  lost,  and  not  a 
particle  of  matter  is  struck  out  of  existence.     The  same  mat- 
ter of  which  every  living  animal,  and  every  vegetable,  was 
formed,  before  and  since  the  flood,  is  still  in  existence.     As 
nothing  is  lost  or  annihilated,  so  it  is  probable  that  nothing 
has  been  added,  and  that  we,  ourselves,  are  composed  of  par- 
ticles of  matter  as  old  as  the  creation.     In  time,  we  must,  in 
our  turn,  suffer  decomposition,  as  all  forms  have  done  before 
us,  and  thus  resign  the  matter  of  which  we  are  composed,  to 
form  new  existences. 

21.  INERTIA. — Inertia  means    passiveness  or  want   of 

When  bodies  suffer  decay,  are  their  particles  lost  1  What  becomes 
of  the  particles  of  bodies  which  decay  7  Is  it  probable  that  any  matter 
has  been  annihilated  or  added,  since  the  first  creation  1  What  is  said 
of  the  particles  of  matter  of  which  we  are  made  1  What  does  inertia 
mean? 


PROPERTIES  OP  BODIES.  13 

power.  Thus  matter  is,  of  itself,  equally  incapable  of  put- 
ting itself  in  motion,  or  of  bringing  itself  to  rest  when  in 
motion. 

22.  It  is  plain  that  a  rock  on  the  surface  of  the  earth, 
never  changes  its  position  in  respect  to  other  things  on  the 
earth.     It  has  of  itself  no  power  to  move,  and  would,  there- 
fore, for  ever  lie  still,  unless  moved  by  some  external  force. 
This  fact  is  proved  by  the  experience  of  every  person,  for 
we  see  the  same  objects  lying  in  the  same  positions  all  our 
lives.     Now,  it  is  just  as  true,  that  inert  matter  has  no  pow- 
3r  to  bring  itself  to  rest,  when  once  put  in  motion,  as  it  is, 
that  it  cannot  put  itself  in  motion,  when  at  rest,  for  having 
no  life,  it  is  perfectly  passive,  both  to  motion  and  rest,  and 
therefore  either  state  depends  entirely  upon  circumstances. 

23.  Common  experience  proving  that  matter  does  not 
put  itself  in  motion,  we  might  be  led  to  believe,  that  rest  is 
the  natural  state  of  all  inert  bodies,  but  a  few  considerations 
will  show,  that  motion  is  as  much  the  natural  state  of  mat- 
ter as  rest,  and  that  either  state  depends  on  the  resistance,  or 
impulse,  of  external  causes. 

24.  If  a  cannon  ball  be  rolled  upon  the  ground,  it  will 
soon  cease  to  move,  because  the  ground  is  rough,  and  pre- 
sents impediments  to  its  motion ;  but  if  it  be  rolled  on  the 
ice,  its  motion  will  continue  much  longer,  because  there  are 
fewer  impediments,  and  consequently,  the  same  force  of  im- 
pulse will  carry  it  much  farther.      We  see  from  this,  that 
with  the  same  impulse,  the  distance  to  which  the  ball  will 
move  must  depend  on  the  impediments  it  meets  with,  or  the 
resistance  it  has  to  overcome.      But  suppose  that  the  ball 
and  ice  were  both  so  smooth  as  to  remove  as  much  as  pos- 
sible the  resistance  caused  by  friction,  then  it  is  obvious  that 
the  ball  would  continue  to  move  longer,  and  go  to  a  greater 
distance.     Next  suppose  we  avoid  the  friction  of  the  ice,  and 
throw  the  ball  through  the  air,  it  would  then  continue  in 
motion  still  longer  with  the  same  force  of  projection,  be- 
cause the  air  alone,  presents  less  impediment  than  the  air 
and  ice,  and  there  is  now  nothing  to  oppose  its  constant  mo- 
tion, except  the  resistance  of  the  air,  and  its  own  weight,  or 
gravity. 

25.  If  the  air  be  exhausted,  or  pumped  out  of  a  vessel  by 

Is  rest  or  motion  the  natural  state  of  matter  7     Why  does  the  ball 
roll  farther  on  the  ice  than  on  the  grqund  1     What  does  this  prore? 
Why,  with  the  same  force  of  projection,  will  a  ball  move  farther  through 
the  air  than  on  the  ice  1 
2 


14  PROPERTIES  OF  BODIES, 

means  of  an  air  pump,  and  a  common  top,  with  a  small,  haid 
point,  be  set  in  motion  in  it,  the  top  will  continue  to  spin  Cor 
hours,  because  the  air  does  not  resist  its  motion.  A  pendu- 
lum, set  in  motion,  in  an  exhausted  vessel,  will  continue  to 
swing,  without  the  help  of  clock  work,  for  a  whole  day,  be- 
cause there  is  nothing  to  resist  its  perpetual  motion,  but  the 
small  friction  at  the  point  where  it  is  suspended,  and  gravity. 

26.  We  see,  then,  that  it  is  the  resistance  of  the  air,  of  fric- 
tion, and  of  gravity,  which  causes  bodies  once  in  motion  to 
cease  moving,  or  come  to  rest,  and  that  dead  matter,  of  itself, 
is  equally  incapable  of  causing  its  own  motion,  or  its  own 
rest. 

27.  We  have  perpetual  examples  of  the  truth  of  this  doc 
trine,  in  the  moon,  and  other  planets.      These  vast  bodies 
move  through  spaces  which  are  void  of  the  obstacles  of  air 
and  friction,  and  their  motions  are  the  same  that  they  were 
thousands  of  years  ago,  or  at  the  beginning  of  creation. 

28.  ATTRACTION. — By  attraction  is  meant  that  property, 
or  quality  in  the  particles" of  bodies,  which  make  them  tend 
toward  each  other. 

29.  We  know  that  substances  are  composed  of   small 
atoms  or  particles  of  matter,  and  that  it  is  a  collection  of  these, 
united  together,  that  forms  all  the  objects  with  which  we  are 
acquainted.     Now,  when  we  come  to  divide,  or  separate  any 
substance  into,  parts,  we  do  not  find  that  its  particles  have 
been  united  or  kept  together  by  glue,  little  nails,  or  any  such 
mechanical  means,  but  that  they  cling  together  by  some 
power,  not  obvious  to  our  senses.     This  power  we  call  at- 
traction, but  of  its  nature  or  cause,  we  are  entirely  ignorant 
Experiment  and  observation,  however,  demonstrate,  that  this 
power  pervades  all  material  things,  and  that  under  different 
modifications,  it  not  only  makes  the  particles  of  bodies  adhere 
to  each  other,  but  is  the  cause  which  keeps  the  planets  in 
their  orbits  as  they  pass  through  the  heavens. 

30.  Attraction  has  received  different  names,  according  to 
the  circumstances  under  which  it  acts. 

31.  The  force  which  keeps  the  particles  of  matter  to- 

Why  will  a  top  spin,  or  a  pendulum  swing,  longer  in  an  exhausted 
vessel  than  in  the  air  1  What  are  the  causes  which  resist  the  perpetual 
motion  of  bodies  7  Where  have  we  an  example  of  continued  motion 
without  the  existence  of  air  and  friction  1  What  is  meant  by  attrac- 
tion'? What  is  known  about  the  cause  of  attraction  7  Is  attraction 
common  to  all  kinds  of  matter,  or  not  1  What  effect  does  this  power 
have  upon  the  planets  7  Why  has  attraction  received  different  namp»  * 


PROPERTIES  OF  BODIES.  15 

gether,  to  form  bodies,  or  masses,  is  called  attraction  of  co- 
hesion That  which  inclines  different  masses  towards  each 
other,  is  called  attraction  of  gravitation.  That  which 
causes  liquids  to  rise  in  tubes,  is  called  capillary  attraction. 
That  which  forces  the  particles  of  substances  of  different 
kinds  to  unite,  is  known  under  the  name  of  chemical  at- 
traction. That  which  causes  the  needle  to  point  constantly 
towards  the  poles  of  the  earth  is  magnetic  attraction  ;  and 
that  which  is  excited  by  friction  in  certain  substances,  is 
known  by  the  name  of  electrical  attraction. 

32.  The  following  illustrations,  it  is  hoped,  will  make 
each  kind  of  attraction  distinct  and  obvious  to  the  mind  of 
the  student. 

33.  ATTRACTION  OF  COHESION  acts  only  at  insensible 
distances,  as  when  the  particles  of  bodies  apparently  touch 
each  other. 

34.  Take  two  pieces  of  lead,  of  a  round  form,  an  inch  in 
diameter,  and  two  inches  long  ;  flatten  one  end  of  each,  and 
make  through  it  an  eye-hole  for  a  string.     Make  the  other 
ends  of  each  as  smooth  as  possible,  by  cutting  them  with  a 
sharp  knife.     If  now  the  smooth  surfaces  be  brought  to- 
gether, with  a  slight  turning  pressure,  they  will  adhere 
with  such  force  that  two  men  can  hardly  pull  them  apart  by 
the  two  strings. 

35.  In  like  manner,  two  pieces  of  plate  glass,  when  their 
surfaces  are  cleaned  from  dust,  and  they  are  pressed  to- 
gether, will  adhere  with  considerable  force.     Other  smooth 
substances  present  the  same  phenomena. 

36.  This   kind  of  attraction  is  much  stronger  in  some 
bodies  than  in  others.     Thus,  it  is  stronger  in  the  metals 
than  in  most  other  substances,  and  in  some  of  the  metals  it 
is  stronger  than  in  others.     In  general,  it  is  most  powerful 
among  the  particles  of  solid  bodies,  weaker  among  those  of 
liquids,  and  probably  entirely  wanting  among  elastic  fluids, 
such  as  air,  and  the  gases. 

37.  Thus,  a  small  iron  wire  will  hold  a  suspended  v^eight 
of  many  pounds,  without  having  its  particles  separated ;  the 

How  many  kinds  of  attraction  are  there  ?  How  does  the  attraction 
of  cohesion  operate  1  What  is  meant  by  attraction  of  gravitation  1 
What  by  capillary  attraction  1  What  by  chemical  attraction  1  What 
is  that  which  makes  the  needle  point  towards  the  pole1?  How  is  elec- 
trical attraction  excited  1  Give  an  example  of  cohesive  attraction  1 
In  what  substances  is  cohesive  attraction  the  strongest  1  In  what  sub- 
stance is  it  weakest  1 


J.6  PROPERTIES  OF  BODIKS. 

particles  of  water  are  divided  by  a  very  small  force,  whil* 
those  of  air  are  still  more  easily  moved  among  each  othei. 
These  different  properties  depend  on  the  force  of  cohesion 
with  which  the  several  particles  of  these  bodies  are  united. 

38.  When  the  particles  of  fluids  are  left  to  arrange  them- 
selves according  to  the  laws  of  attraction,  the  bodies  which 
they  compose  assume  the  form  of  a  globe  or  ball. 

39.  Drops  of  water  thrown  on  an  oiled  surface  or  on  wax 
— globules  of  mercury, — hail  stones, — a  drop  of  water  ad- 
hering to  the  end  of  the  finger, — tears  running  down  the 
cheeks,  and  dew  drops   on   the   leaves  of  plants,  are  all 
examples  of  this  law  of  attraction.    The  manufacture  of  shot 
is  also  a  striking  illustration.      The  lead   is  melted  and 
poured  into  a  sieve,  at  the  height  of  about  two  hundred  feet 
from  the  ground.     The  stream  of  lead,  immediately  after 
leaving  the  sieve,  separates  into  round  globules,  which,  be- 
fore they  reach  the  ground,  are  cooled  and  become  solid, 
and  thus  are  formed  the  shot  used  by  sportsmen. 

40.  To  account  for  the  globular  form  in  all  these  cases, 
we  have  only  to  consider  that  the  particles  of  matter  are 
mutually  attracted  towards  a  common  centre,  and  in  liquids 
being  free  to  move,  they  arrange  themselves  accordingly. 

41.  In  all  figures  except  the  globe,  or  ball,  some  of  the 
particles  must  be  nearer  the  centre  than  others.     But  in  a 
body  that  is  perfectly  round,  every  part  of  the  outside  is 
exactly  at  the  same  distance  from  the  centre. 

42.  Thus,  the  corners  of  a  cube,  or  Fig.  1. 
square,  are  at   much   greater  distances 

from  the  centre,  than  the  sides,  while  the 

circumference  of  a  circle  or  ball  is  every  / 

where  at  the  same  distance  from  it.  This  [ 

difference  is  shown  by  fig.  1,  and  it  is  \ 

quite   obvious,  that  if  the   particles  of  \ 

matter  are  equally  attracted  towards  the 

common  centre,  and  are  free  to  arrange 

themselves,  no  other  figure  could  possibly  be  formed,  since 

then  every  part  of  the  outside  is  equally  attracted. 

43.  The  sun,  earth,  moon,  and  indeed  all  the  heavenly 

Whv  are  the  particles  of  fluids  more  easily  separated  than  those  of 
Bohds  1  What  form  do  fluids  take,  when  their  particles  are  left  to  their 
own  arrangement  7  Give  examples  of  this  law.  How  is  the  globular 
form  which  liquids  assume  accounted  for1?  If  the  particles  of  a  body 
are  free  to  move,  and  are  equally  attracted  towards  the  centre,  what 
must  be  its  figure  1  Why  must  the  figure  be  a  globe? 


PROPERTIES  OF  BODIES. 


17 


Fi<r.  2. 


bodies,  are  illustrations  of  this  law,  and  therefore  were  pro- 
bably in  so  soft  a  state  when  first  formed,  as  to  allow  their 
particles  freely  to  arrange  themselves  accordingly. 

44.  ATTRACTION  OF  GRAVITATION. — As  the  attraction  of 
cohesion  unites  the  particles  of  matter  into  masses  or  bodies, 
so  the  attraction  of  gravitation  tends  to  force  these  masses 
towards  each  other,  to  form  those  of  still  greater  dimensions. 
The  term  gravitation,  does  not  here  strictly  refer  to  the 
weight  of  bodies,  but  to  the  attraction  of  the  masses  of  matter 
towards  each  other,  whether  downwards,  upwards,  or  hori- 
zontally. 

45.  The  attraction  of  gravitation   is  mutual,  since  all 
bodies  not  only  attract  other  bodies,  but  are  themselves  at- 
tracted. 

46.  Two  cannon  balls,  when  suspended  by 
long  cords,  so  as  to  hang  quite  near  each  other, 
are  found  to  exert  a  mutual  attraction,  so  that 
neither  of  the  cords  is  exactly  perpendicular 
but  they  approach  each  other,  as  in  fig.  2. 

47.  In  the  same  manner,  the  heavenly  bo- 
dies, when  they  approach  each  other,  are  drawn 
out  of  the  line  of  their  paths,  or  orbits,  by  mu- 
tual attraction. 

48.  The  force  of  attraction  increases  in  pro- 
portion as  bodies  approach  each  other,  and  by 
the  same  law  it  must  diminish  in  proportion  as 
they  recede  from  each  other. 

49.  Attraction,  in  technical  language,  is  in- 
versely as  the  squares  of  the  distances  between 
the  two  bodies.     That  is,  in  proportion  as  the 
square  of  the  distance  increases,  in  the  same 
proportion  attraction  decreases,  and  so  the  contrary.     Thus, 
if  at  the  distance  of  2  feet,  the  attraction  be  equal  to  4  pounds, 
at  the  distance  of  4  feet,  it  will  be  only  1  pound ;  for  the 
square  of  2  is  4,  and  the  square  of  4  is  16,  which  is  4  times 
the  square  of  2.     On  the  contrary,  if  the  attraction  at  the 
distance  of  6  feet  be  3  pounds,  at  the  distance  of  2  feet  it 
will  be  9  times  as  much,  or  27  pounds,  because  36,  the 
square  of  6,  is  equal  to  9  times  4,  the  square  of  2. 

What  great  natural  bodies  are  examples  of  this  law  7  What  is  meant 
by  attraction  of  gravitation  1  Can  one  body  attract  another  without 
beinq;  itself  attracted  1  How  is  it  proved  that  bodies  attract  each  other  7 
By  what  law,  or  rule,  does  the  force  of  attraction  increase  1  Give  an 
example  of  this  rule. 


18 


PROPERTIES  OF  BODIES. 


50.  The  intensity  of  light  is  found  to  incn?ase  and  tti 
minish  in  the  same  proportion.     Thus,  if  a  Iboard  a  foo* 
square,  be  placed  at  the  distance  of  one  foot  from  a  candle, 
it  will  be  found  to  hide  the  light  from  another  tward  of  two 
feet  square,  at  the  distance  of  two  feet  from  the  candle.  Now 
a  board  of  two  feet  square  is  just  four  times  as  large  as  one 
of  one  foot  square,  and  therefore  the  light  at  double  the  dis- 
tance being  spread  over  4  times  the  surface,  has  only  one 
fourth  the  intensity. 

51.  The  expe-  Fig.  3. 
riment  may  be  ea- 
sily tried,  or  may 

be  readily  under- 
stood by  fig.  3, 
where  c  repre- 
sents the  candle, 
A,  the  small 

board,  and  B  the  large  one ;  B  being  four  'times  the  size 
of  A. 

The  force  of  the  attraction  of  gravitation,  is  in  proportion 
to  the  quantity  of  matter  the  attracting  body  contains. 

Some  bodies  of  the  same  bulk  contain  a  much  greater 
quantity  of  matter  than  others  :  thus,  a  piece  of  lead  con- 
tains about  twelve  times  as  much  matter  as  a  piece  of  cork 
of  the  same  dimensions,  and  therefore  a  piece  of  lead  of  any 
given  size,  and  a  piece  of  cork  twelve  times  as  large,  will 
attract  each  other  equally. 

52.  CAPILLARY  ATTRACTION. — The  force  by  which 
small  tubes,  or  porous  substances,  raise  liquids  above  their 
levels,  is  called  capillary  attraction. 

If  a  small  glass  tube  be  placed  in  water,  trie  water  on  the 
inside  will  be  raised  above  the  level  of  that  01.1  the  outside  of 
the  tube.  The  cause  of  this  seems  to  be  nothing  more  than 
the  ordinary  attraction  of  the  particles  of  matter  for  each 
other.  The  sides  of  a  small  orifice  are  so  near  each  other, 
as  to  attract  the  particles  of  the  fluid  on  their  opposite  sides, 
and  as  all  attraction  is  strongest  in  the  direction  of  the 


How  is  it  shown  that  the  intensity  of  light  increases  and  diminishes 
in  the  same  proportion  as  the  attraction  of  matter  1  Do  bodies  attract 
in  proportion  to  bulk,  or  quantity  of  matter  1  What  would  be  the  dif- 
ference of  attraction  between  a  cubic  inch  of  lead,  and  a  cubic  inch  of 
cork  7  Why  would  there  be  so  much  difference  1  What  is  meant  by 
capillary  attraction  ?  How  is  this  kind  of  attraction  illustrated  with 
a  glass  tube  1 


PROPE    TIES  OF  BODIE*.  19 

jpreatest  quantity  of  matter,  the  water  is  raised  upwards,  or 
in  the  direction  of  the  length  of  the  tube.  On  the  outside 
of  the  tube,  the  opposite  surfaces,  it  is  obvious,  cannot  act 
on  the  same  column  of  water,  and  therefore  the  influence 
of  attraction  is  here  hardly  perceptible  in  raising  the  fluid. 
This  seems  to  be  the  reason  why  the  fluid  rises  higher  on 
the  inside  than  on  the  outside  of  the  tube. 

53.  A  great  variety  of  porous  substances  are  capable  of 
this  kind  of  attraction.     If  a  piece  of  sponge  or  a  lump  of 
sugar  be  placed,  so  that  its  lowest  corner  touches  the  water, 
the  fluid  will  rise  up  and  wet  the  whole  mass.    In  the  same 
manner,  the  wick  of  a  lamp  will  carry  up  the  oil  to  supply 
the  flame,  though  the  flame  is  several  inches  above  the  level 
of  the  oil.     If  the  end  of  a  towel  happens  to  be  left  in  a 
basin  of  water,  it  will  empty  the  basin  of  its  contents.    And 
on  the  same  principle,  when  a  dry  wedge  of  wood  is  driven 
into  the  crevice  of  a  rock,  and  afterwards  moistened  with 
water,  as  when  the  rain  falls  upon  it,  it  will  absorb  the 
water,  swell,  and  sometimes  split  the  rock.     In  Germany, 
mill-stone  quarries  are  worked  in  this  manner. 

54.  CHEMICAL  ATTRACTION  takes   place   between  the 
particles  of  substances  of  different  kinds,  and  unites  them 
into  one  compound. 

•  55.  This  species  of  attraction  takes  place  only  between 
the  particles  of  certain  substances,  and  is  not,  therefore,  a 
universal  property.  It  is  also  known  under  the  name  of 
chemical  affinity,  because  it  is  said,  that  the  particles  of  sub- 
stances having  an  affinity  between  them,  will  unite,  while 
those  having  no  affinity  for  each  other  do  not  readily  enter 
into  union. 

56.  There  seems,  indeed,  in  this  respect,  to  be  very  sin- 
gular preferences,  and  dislikes,  existing  among  the  particle1! 
of  matter.  Thus,  if  a  piece  of  marble  be  thrown  into  sul- 
phuric acid,  their  particles  will  unite  with  great  rapidity 
and  commotion,  and  there  will  result  a  compound  differing 
in  all  respects  from  the  acid  or  the  marble.  But  if  a  piece 
of  glass,  quartz,  gold,  or  silver,  be  thrown  into  the  acid,  no 
change  is  produced  on  either,  because  their  particles  have 
no  affinity. 

Why  does  the  water  rise  higher  in  the  tube  than  it  does  on  the  out- 
side? Give  some  common  illustrations  of  this  principle.  What  is  the 
effect  of  chemical  attraction  7  By  what  other  name  is  this  kind  of  at- 
traction known  1  What  effect  is  produced  when  marble  and  sulphuric 
acid  are  brought  together  ?  What  is  the  effect  when  glass  and  this 
acid  are  brought  together  ?  What  is  the  reason  of  this  difference  1 


20  PROPERTIES  OF  BODIES. 

Sulphur  and  quicksilver,  when  heated  together,  will  form 
a  beautiful  red  compound,  known  under  the  name  of  ver- 
milion, and  which  has  none  of  the  qualities  of  sulphur  or 
quicksilver. 

57.  Oil  and  water  have  no  affinity  for  each  other,  but 
potash  has  an  attraction  for  both,  and  therefore  oil  and  water 
will  unite  when  potash  is  mixed  with  them.     In  this  man- 
ner, the  well  known  article  called  soap  is  formed.     But  the 
potash  has  a  stronger  attraction  for  an  acid  than  it  has  for 
either  the  oil  or  the  water ;    and  therefore  when  soap  is 
mixed  with  an  acid,  the  potash  leaves  the  oil,  and  unites 
with  the  acid,  thus  destroying  the  old  compound,  and  at  the 
same  instant  forming  a  new  one.     The  same  happens  when 
soap  is  dissolved  in  any  water  containing  an  acid,  as  the 
water  of  the  sea,  and  of  certain  wells.     The  potash  forsakes 
the  oil,  and  unites  with  the  acid,  thus  leaving  the  oil  to  rise 
to  the  surface  of  the  water.     Such  waters  are  called  hard, 
and  will  not  wash,  because  the  acid  renders  the  potash  a 
neutral  substance. 

58.  MAGNETIC  ATTRACTION. — There  is  a  certain  ore  of 
iron,  a  piece  of  which,  being  suspended  by  a  thread,  will 
always  turn  one  of  its  sides  to  the  north.     This  is  called  the 
load-stone,  or  natural  Magnet,  and  when  it  is  brought  near 
a  piece  of  iron,  or  steel,  a  mutual  attraction  takes  place,  and 
under  certain  circumstances,  the  two  bodies  will  come  to- 
gether and  adhere  to  each  other.     This  is  called  Magnetic 
Attraction.     When  a  piece  of  steel  or  iron  is  rubbed  with 
a  Magnet,  the  same  virtue  is  communicated  to  the  steel,  and 
it  will  attract  other  pieces  of  steel,  and  if  suspended  by^a 
string,  one  of  its  ends  will  constantly  point   towards   trie 
north,  while  the  other,  of  course,  points  towards  the  south. 
This  is  called  an  artificial  Magnet.     The  magnetic  needle 
is  a  piece  of  steel,  first  touched  with  the  loadstone,  and  then 
suspended,  so  as  to  turn  easily  on  a  point.    By  means  of  this 
instrument,  the  mariner  guides  his  ship,  through  the  path- 
less ocean.     See  Magnetism. 

59.  ELECTRICAL  ATTRACTION. — When  a  piece  of  glass, 
or  sealing  wax,  is  rubbed  with  the  dry  hand,  or  a  piece  of 


How  may  oil  and  water  be  made  to  unite?  What  is  the  composi 
tion  thus  formed  called  1  How  does  an  acid  destroy  this  compound » 
What  is  the  reason  that  hard  water  will  not  wash  ?  What  is  a  na 
:ural  magnet  ?  What  is  meant  by  magnetic  attraction  1  What  is  at 
artificial  magnet 7  What  is  a  magnetic  needle?  What  is  its  use: 
What  is  meant  by  electrical  attraction  J 


PROPERTIES  OF  BODIES.  21 

cloth,  and  then  held  towards  any  light  substance,  such  as 
hair,  or  thread,  the  light  body  will  be  attracted  by  it,  and 
will  adhere  for  a  moment  to  the  glass  or  wax.  The  influ- 
ence which  thus  moves  the  light  body  is  called  Electrical 
Attraction.  When  the  light  body  has  adhered  to  the  sur- 
face of  the  glass  for  a  moment,  it  is  again  thrown  of£  or 
repelled,  and  this  is  called  Electrical  Repulsion.  See  Elec- 
tricity. 

60.  We  have  thus  described  and  illustrated  all  the  uni- 
versal or  inherent  properties  of  bodies,  and  have  also  no- 
ticed the  several   kinds  of  attraction  which  are  peculiar, 
namely,  Chemical,  Magnetic,  and  Electrical.     There  are 
still  several   properties   to   be  mentioned.     Some  of  them 
belong  to  certain  bodies  in  a  peculiar  degree,  while  other 
bodies  possess  them  but  slightly.    Others  belong  exclusively 
to  certain    substances,  and  not  at   all   to   others.      These 
properties  are  as  follows. 

61.  DENSITY. — This  property  relates  to  the  compactness 
of  bodies,  or  the  number  of  particles  which  a  body  contains 
within  a  given  bulk.     It  is  closeness  of  texture.     Bodies 
which  are  most  dense,  are  those  which  contain  the  least 
number  of  pores.     Hence  the  density  of  the  metals  is  much 
greater  than  the  density  of  wood.     Two  bodies  being  of 
equal  bulk,  that  which  weighs  most,  is  most  dense.     Some 
of  the  metals  may  have  this  quality  increased  by  hammer- 
ing, by  which  their  pores  are  filled  up  and  their  particles 
are  brought  nearer  to  each  other.     The  density  of  air  is 
increased  by  forcing  more  into  a  close  vessel  than  it  natu- 
rally contained. 

62.  RARITY. — This  is  the  quality  opposite  to  density, 
and  means  that  the  substance  to  which  it  is  applied  is  po- 
rous, and  light.     Thus  air,  water,  and  ether,  are  rare  sub- 
stances, while  gold,  lead,  and  platina,  are  dense  bodies. 

63.  HARDNESS. — This  property  is  not  in  proportion,  as 
might  be  expected,  to  the  density  of  the  substance,  but  to  the 
force  with  which  the  particles  of  a  body  cohere,  or  keep 
their  places.     Glass,  for  instance,  will  scratch  gold  or  pla- 
tina, though  these  metals  are  much  more  dense  than  glass. 
It   is   probable,  therefore,  that   these   metals    contain  the 

What  is  electrical  repulsion  1  What  is  density  ?  What  bodies  are 
most  dense1?  How  may  this  quality  be  increased  in  the  metals'?  What 
is  rarity  *?  What  are  rare  bodies  7  What  are  dense  bodies  1  How 
does  hardness  differ  from  density  1  Why  will  glass  scratch  gold  or 
platina  1 


22  PROPERTIES  OP  BODIES. 

greatest  number  of  particles,  but  that  those  of  the  glass  are 
more  firmly  fixed  in  their  places. 

Some  of  the  metals  can  be  made  hard  or  soft  at  pleasure. 
Thus  steel  when  heated,  and  then  suddenly  cooled,  becomes 
harder  than  glass,  while  if  allowed  to  cool  slowly,  it  is  soil 
and  flexible. 

64.  ELASTICITY  is  that  property  in  bodies  by  which, 
after  being  forcibly  compressed  or  bent,  they  regain  their 
original  state  when  the  force  is  removed. 

Some  substances  are  highly  elastic,  while  others  want 
this  property  entirely.  The  separation  of  two  bodies  after 
impact,  or  striking  together,  is  a  proof  that  one  or  both  are 
elastic.  In  general,  most  hard  and  dense  bodies,  possess 
this  quality  in  greater  or  less  degree.  Ivory,  glass,  marble, 
flint,  and  ice,  are  elastic  solids.  An  ivory  ball,  dropped 
upon  a  marble  slab,  will  bound  nearly  to  the  height  from 
which  it  fell,  arid  no  mark  will  be  left  on  either.  India 
rubber  is  exceedingly  elastic,  and  on  being  thrown  for- 
cibly against  a  hard  body,  will  bound  to  an  amazing 
distance. 

Putty,  dough,  and  wet  clay,  are  examples  of  the  entire 
want  of  elasticity,  and  if  either  of  these  be  thrown  against 
an  impediment,  they  will  be  flattened,  stick  to  the  place 
they  touch,  and  never,  like  elastic  bodies,  regain  their  for- 
mer shapes. 

Among  fluids,  water,  oil,  and  in  general  all  such  sub- 
stances as  are  denominated  liquids,  are  nearly  inelastic, 
while  air  and  the  gaseous  fluids,  are  the  most  elastic  of  all 
bodies. 

65.  BRITTLENESS  is  the  property  which  renders  sub- 
stances easily  broken,  or  separated  into  irregular  fragments. 
This  property  belongs  chiefly  to  hard  bodies. 

It  does  not  appear  that  brittleness  is  entirely  opposed  to 
elasticity,  since  in  many  substances,  both  these  properties 
are  united.  Glass  is  the  standard,  or  type  of  brittleness,  and 
yet  a  ball,  or  fine  threads  of  this  substance,  are  highly  elas- 
tic, as  may  be  seen  by  the  bounding  of  the  one,  and  the 
springing  of  the  other.  Brittleness  often  results  from  the 

What  metal  can  be  made  hard  or  soft  at  pleasure  1  What  is  meant 
by  elasticity  1  How  is  it  known  that  bodies  possess  this  property  7 
Mention  several  elastic  solids.  Give  examples  of  inelastic  solids.  Do 
liquids  possess  this  property  7  What  are  the  most  elastic  of  all  sub- 
stances 1  What  is  brittleness '?  Are  brittleness  and  elasticity  ever 
found  in  the  same  substance  1  Give  examples. 


PROPERTIES  OP  BODIES,  23 

treatment  to  which  substances  are  submitted.  Iron,  steel, 
brass,  and  copper,  become  brittle  when  heated  and  suddenly 
cooled;  but  if  cooled  slowly,  they  are  not  easily  broken. 

66.  MALLEABILITY. — Capability  of  being  drawn  under 
the  hammer,  or  rolling-  press.     This  property  belongs  to 
some  of  the  metals,  but  not  to  all,  and  is  of  vast  importance 
to  the  arts  and  conveniences  of  life. 

The  Malleable  metals  are,  gold,  silver,  iron,  copper,  and 
some  others.  Antimony,  bismuth,  and  cobalt,  are  brittle 
metals.  Brittleness  is  therefore  the  opposite  of  malleability. 

Gold  is  the  most  malleable  of  all  substances.  It  may  be 
drawn  under  the  hammer  so  thin  that  light  may  be  seen 
through  it.  Copper  and  silver  are  also  exceedingly  malle- 
able. 

67.  DUCTILITY,  is  that  property  in  substances  which  ren- 
ders them  susceptible  of  being  drawn  into  wire. 

We  should  expect  that  the  most  malleable  metals  would 
also  be  the  most  ductile  ;  but  experiment  proves  that  this  is 
not  the  case.  Thus,  tin  and  lead  may  be  drawn  into  thin 
•eaves,  but  cannot  be  drawn  into  small  wire.  Gold  is  the 
most  malleable  of  all  the  metals,  but  platina  is  the  most 
ductile.  Dr.  Wollaston  drew  platina  into  threads  not  much 
larger  than  a  spider's  web. 

68.  TENACITY,  in  common  language  called  toughness, 
refers  to  the  force  of  cohesion  among  the  particles  of  bodies. 
Tenacious  bodies  are  not  easily  pulled  apart.     There  is  a 
remarkable  difference  in  the  tenacity  of  different  substances. 
Some  possess  this  property  in  a  surprising  degree,  while 
others  are  torn  asunder  by  the  smallest  force. 

Among  the  malleable  metals,  iron  and  steel  are  the  most 
tenacious,  while  lead  is  the  least  so.  Steel  is  by  far  the  most 
tenacious  of  all  known  substances.  A  wire  of  this  metal, 
no  larger  than  the  hundredth  part  of  an  inch  in  diameter, 
sustained  a  weight  of  134  pounds,  while  a  wire  of  platina  of 
the  same  size  would  sustain  a  weight  of  only  16  pounds, 
and  one  of  lead  only  2  pounds.  Steel  wire  will  sustain 
39,000  feet  of  its  own  length  without  breaking. 


How  are  iron,  steel,  and  brass,  made  brittle  1  What  does  mallea- 
bility mean  7  What  metals  are  malleable,  and  what  ones  are  brittle  7 
Which  is  the  most  malleable  metal  1  What  is  meant  by  ductility  1 
Are  the  most  malleable  metals  the  most  ductile  7  What  is  meant  by 
tenacity  1  From  what  does  this  property  arise*?  What  metals  are 
most  tenacious  1  What  proportion  does  the  tenacity  of  steel  bear  to 
that  of  platina  and  lead  1 


24  GRAVITY. 

69.  RECAPITULATION. — The  common,  or  essential  pro- 
perties of  bodies,  are,  Impenetrability,  Extension,  Figure, 
Divisibility,  Inertia,  and  Attraction.    Attraction  is  of  several 
kinds,  namely,  Attraction  of  cohesion,  Attraction  of  gravita- 
tion, Capillary  attraction,  Chemical  attraction,  Magnetic  at- 
traction, and  Electrical  attraction. 

70.  The  peculiar  properties  of  bodies  are,  Density,  Rari- 
ty, Hardness,  Elasticity,  Brittleness,  Malleability,  Ductility, 
and  Tenacity. 

FORCE  OF  GRAVITY. 

71.  The  force  by  which  bodies  are  drawn  towards  each 
other  in  the  mass,  and  by  which  they  descend  towards  the 
earth  when  suspended  or  let  fall  from  a  height,  is  called  the 
force  of  gravity.  (43.) 

72.  The  attraction  which  the  earth  exerts  on  all  bodies 
near  its  surface,  is  called  terrestrial  gravity,  and  the  force 
with  which  any  substance  is  drawn  downwards,  is  called  its 
weight. 

73.  All  falling  bodies  tend  downwards  towards  the  centre 
of  the  earth,  in  a  straight  line  from  the  point  where  they  arc 
let  fall.     If  then  a  body  be  let  fall  in  any  part  of  the  world, 
the  line  of  its  direction  will  be  perpendicular  to  the  earth's 
surface.     It  follows,  therefore,  that  two  falling  bodies,  on 
opposite  parts  of  the  earth,  mutually  fall  towards  each  other. 

74.  Suppose  a  cannon  ball  to  be  disengaged  from  a  height 
opposite  to  us,  on  the  other  side  of  the  earth,  its  motion  in 
respect  to  us,  would  be  upward,  while  the  downward  motion 
from  where  we  stand,  would  be  upward  in  respect  to  those 
who  stand  opposite  to  us,  on  the  other  side  of  the  earth. 

75.  In  like  manner,  if  the  falling  body  be  a  quarter,  in- 
stead of  half  the  distance  round  the  earth  from  us,  its  line 
of  direction  would  be  directly  across,  or  at  right  angles  with 
the  line  already  supposed. 

"What  are  the  essential  properties  of  bodies  1  How  many  kinds  of 
attraction  are  there  7  What  are  the  peculiar  properties  of  bodies  1 
What  is  gravity  1  What  is  terrestrial  gravity  ?  To  what  point  in  the 
earth  do  falling  bodies  tend  1  In  what  direction  will  two  falling  bo- 
dies from  opposite  parts  of  the  earth  tend,  in  respect  to  each  other "?  In 
what  direction  will  one  from  half  way  between  them  meet  their 
'ine? 


GRAVITY. 

76.  This  will  be  readily  Fig.  4. 

understood  by  fig.  4,  where 
the  circle  is  supposed  to  be 
the  circumference  of  the 
earth,  a,  the  ball  falling  to- 
wards its  upper  surface, 
where  we  stand ;  b,  a  ball 
falling  towards  the  oppo- 
site side  of  the  earth,  but 
ascending  in  respect  to  us; 
and  d,  a  ball  descending  at 
the  distance  of  a  quarter  of 
the  circle,  from  the  other 
two,  and  crossing  the  line 
of  their  direction  at  right 
angles. 

77.  It  will  be  obvious, 

therefore,  that  what  we  call  up  and  down  are  merely  relative 
terms,  and  that  what  is  down  in  respect  to  us,  is  up  in  re- 
spect to  those  who  live  on  the  opposite  side  of  the  earth,  and 
so  the  contrary.  Consequently,  down  every  where  means  to- 
wards the  centre  of  the  earth,  and  up  from  the  centre  of  the 
earth ;  because  all  bodies  descend  towards  the  earth's  centre, 
from  whatever  part  they  are  let  fall.  This  will  be  apparent 
when  we  consider,  that  as  the  earth  turns  over  every  24 
hours,  we  are  carried  with  it  through  the  points  a,  d,  and  b, 
fig.  4 ;  and  therefore,  if  a  ball  is  supposed  to  fall  from  the 
point  a,  say  at  12  o'clock,  and  the  same  ball  to  fall  again 
from  the  same  point  above  the  earth,  at  6  o'clock,  the  two 
lines  of  direction  will  be  at  right  angles,  as  represented  in 
the  figure,  for  that  part  of  the  earth  which  was  under  a  at 
12  o'clock,  will  be  under  d  at  6  o'clock,  the  earth  having 
in  that  time  performed  one  quarter  of  its  daily  revolution. 
At  12  o'clock  at  night,  if  the  ball  be  supposed  to  fall  again, 
its  line  of  direction  will  be  at  right  angles  with  that  of  its 
last  descent,  and  consequently  it  will  ascend  in  respect  to 
the  point  on  which  it  fell  12  hours  before,  because  the  earth 
would  have  then  gone  through  one  half  her  daily  rotation, 
and  the  point  a  would  be  at  b. 

How  is  this  shown  by  the  figure  1  Are  the  terms  up  and  down  rela- 
tive, or  positive,  in  their  meaning  1  What  is  understood  by  down  in 
any  part  of  the  earth  1  Suppose  a  ball  be  let  fall  at  12  and  then  at  6 
o'clock,  in  what  direction  would  the  lines  of  their  descent  meet  each 
other'?  Suppose  two  balls  to  descend  from  opposite  sides  of  the  earth, 
what  would  be  their  direction  in  respect  to  each  other  1 
8 


26  GRAVITY. 

The  velocity  or  rapidity  of  every  falling  body,  is  uni- 
formly accelerated,  or  increased,  in  its  approach  towards 
the  earth,  from  whatever  height  it  falls. 

78.  If  a  rock  is  rolled  from  a  steep  mountain,  its  motion 
is  at  first  slow  and  gentle,  but  as  it  proceeds  downward,  it 
moves  with  perpetually  increased  velocity,  seeming  to  gath- 
er fresh  speed  every  moment,  until  its  force  is  such  that 
every  obstacle  is  overcome ;  trees  and  rocks  are  beat  from 
its  path,  and  its  motion  does  not  cease  until  it  has  rolled  to 
a  great  distance  on  the  plain. 

VELOCITY  OF  FALLING  BODIES. 

79.  The  same  principle  of  increased  velocity  as  bodies 
descend  from  a  height,  is  curiously  illustrated  by  pouring 
molasses  or  thick  syrup  from  an  elevation  to  the  ground. 
The  bulky  stream,  of  perhaps  two  inches  in  diameter,  where 
it  leaves  the  vessel,  as  it  descends,  is  reduced  to  the  size  of 
a  straw,  or  knitting  needle ;  but  what  it  wants  in  bulk  is 
made  up  in   velocity,  for  the  small  stream  at  the  ground, 
will  fill  a  vessel  just  as  soon  as  the  large  one  at  the  outlet. 

80.  For  the  same  reason,  a  man  may  leap  from  a  chair 
without  danger,  but  if  he  jumps  from  the  house  top,  his 
velocity  becomes  so  much  increased,  before  he  reaches  the 
ground,  as  to  endanger  his  life  by  the  blow. 

It  is  found  by  experiment,  that  the  motion  of  a  falling 
body  is  increased,  or  accelerated,  in  regular  mathematical 
proportions. 

81.  These  increased  proportions  do  not  depend  on  the 
increased  weight  of  the  body,  because  it  approaches  nearer 
the  centre  of  the  earth,  but  on  the  constant  operation  of  the 
force  of  gravity",  which  perpetually  gives  new  impulses  to 
the  falling  body,  and  increases  its  velocity. 

82.  It  has  been  ascertained  by  experiment,  that  a  body, 
falling  freely,  and  without  resistance,  passes  through  a  space 
of  16  feet  and  1  inch  during  the  first  second  of  time.    Leav- 
ing out  the  inch,  which  is  not  necessary  for  our  present 
purpose,  the  ratio  of  descent  is  as  follows., 

83.  If  the  height  through  which  a  body  falls  in  one  se- 
cond of  time  be  known,  the  height  which  it  falls  in  any 

What  is  said  concerning  the  motions  of  falling  bodies  *?  How  is 
this  increased  velocity  illustrated  1  Why  is  there  any  more  danger  in 
jumping  from  the  house  top  than  from  a  chair  1  What  number  of  feet 
does  a  falling  body  pass  through. 


GRAVITY.  27 

proposed  time  may  be  computed.  For  since  the  height  is 
proportional  to  the  square  of  :ne  time,  the  height  through 
which  it  will  fall  in  two  seconds  will  be  four  times  that 
which  it  falls  through  in  one  second.  In  three  seconds  it 
will  fall  through  nine  times  that  space ;  in  four  seconds, 
sixteen  times  that  of  the  first  second  ;  in  five  seconds,  twenty- 
five  times,  and  so  on  in  this  proportion. 

84.  The  following,  therefore,  is  a  general  rule  to  find 
the  height  through  which  a  body  will  fall  in  any  given 
time. 

85.  Rule. — Reduce  the  given  time  to  seconds ;  take  the 
square  of  the  number  of  seconds  in  the  time,  and  multiply 
the  height  through  which  the  body  falls  in  one  second  by 
that  number,  and  the  result  will  be  the  height  sought. 

86.  The  following  table  exhibits  the  height  and  corres- 
ponding times  as  far  as  10  seconds. 


Time 
Height 

1 
1 

2 

4 

3 

9 

4 
16 

5 

25 

6 
36 

7 
49 

8 
64 

9 

81 

10 
100 

87.  Each  unit  in  the  upper  row  expresses  a  second  of  time, 
and  each  unit  in  those  of  the  second  row  expresses  the 
height  through  which  a  body  falls  freely  in  a  second. 

88.  Now,  as  the  body  falls  at  the  rate  of  16  feet  during 
the  first  second,  this  number,  according  to  the  rule,  multi- 
plied by  the  square  of  the  time,  that  is,  by  the  numbers  ex- 
pressed in  the  second  line,  will  show  the  actual  distance 
through  which  the  body  falls. 

89.  Thus  we  have  for  the  first  second  16  feet;  for  the 
end  of  the  second,  4X16=64  feet;  third,  9X16-144;  fourth, 
16X16=256;  fifth,  25X16=400;  sixth,  36X16=576;  sev- 
enth, 49X16=784;  and  for  the  10  seconds  1600  feet. 

90.  If,  on  dropping  a  stone  from  a  precipice,  or  into  a 
well,  we  count  the  seconds  from  the  instant  of  letting  it  fall 
until  we  hear  it  strike,  we  may  readily  estimate  the  height 
of  the  precipice,  or  the  depth  of  the  well.     Thus,  suppose  it 
is  5  seconds  in  falling,  then  we  only  have  to  square  the 
seconds,  and  multiply  this  by  the  distance  the  body  falls  in 
one  second.     We  have  then  5X5=25,  the  square,   which 
25X16=246  feet,  the  depth  of  the  well. 

91.  Thus  it  appears,  that  to  ascertain  the  velocity  with 

If  a  body  fall  from  a  certain  height  in  two  seconds,  what  proportion 
to  this  will  it  fall  in  four  seconds  7  What  is  the  rule  by  which  the 
height  from  which  a  body  falls  may  be  found  1  How  many  feet  does 
a  body  fall  in  one  second  1  How  many  feet  will  a  body  fall  in  nine 
seconds. 


28 


GRAVITY. 


which  a  body  falls  in  any  given  time,  we  must  know  how 
many  feet  it  fell  during  the  first  second.  The  velocity  ac- 
quired in  one  second,  and  the  space  fallen  through  during 
that  time,  being  the  fundamental  elements  of  the  whole  cal- 
culation, and  all  that  are  necessary  for  the  computation  of 
the  various  circumstances  of  falling  bodies. 

92.  The  difficulty  of  calculating  exactly  the  velocity  of 
a  falling  body  from  an  actual  measurement  of  its  height, 
and  the  time  which  it  takes  to  reach  the  ground,  is  so  great, 
that  no  accurate  computation  could  be  made  from  such  an 
experiment. 

93.  Atwoodls   Machine. — This   difficulty  has,  however, 
been  overcome  by  a  curious  piece  of  machinery,  invented 
for  this  purpose  by  Mr.  Atwood. 


94.  This  machine  consists 
of  two  upright  posts  of  wood, 
fig.    5,   with   cross   pieces,  as 
shown   in   the    figure.      The 
weights  A  and  JB,  are  of  the 
same  size,  and  made  to  balance 
each  other  very  exactly,  and 
are   connected    by  the   thread 
which  passes  over  the  wheel 
C.  F  is  a  ring  through  which 
the  weight  A  passes,  and  G  is 
a  stage  on  which  the  weight 
rests  in  its  descent.     The  ring 
and  stage  both   slide  up  and 
down,  and  are  fixed  at  pleasure 
by  thumb  screws.     The  post 
H,  is  a  graduated  scale,  and 
the   pendulum   K,  is   kept  in 
motion  by  clock-work.    L,  is  a 
small  bar  of  metal,  weighing  a 
quarter  of  an  ounce,  and  long- 
er  than   the   diameter  of  the 
ring  JP. 

95.  When  the  machine  is  to 
oe  used,  the  weight  A  is  drawn 
up  to  the  top  of  the  scale,  and 
the  ring  and  stage  are  placed 
a   certain    number   of  inches 


Fig.  5. 


H  I 


* 


Is  the  velocity  of  a  falling  body  calculated  from  actual  measurement, 
or  by  a  machine  1  Describe  the  operation  of  Mr.  Atwood's  machin* 
for  estimating  the  velocities  of  falling  bodies. 


GRAVITY.  29 

from  each  other.  The  small  bar  JL,  is  then  placed  across 
the  weight  A,  by  means  of  which  it  is  made  slowly  to  de- 
scend. When  it  has  descended  to  the  ring,  the  small  weight 
L,  is  taken  off  by  the  ring,  and  thus  the  two  weights  are  left 
equal  to  each  other.  Now  it  must  be  observed,  that  the 
motion,  and  descent  of  the  weight  A,  is  entirely  owing  to 
the  gravitating  force  of  the  weight  L,  until  it  arrives  at  the 
ring  F,  when  the  action  of  gravity  is  suspended,  and  the 
large  weight  continues  to  move  downwards  to  the  stage,  in 
consequence  of  the  velocity  it  had  acquired  previously  to 
that  time. 

96.  To  comprehend  the  accuracy  of  this  machine,  it  must 
be  understood  that  the  velocities  of  gravitating  bodies  are 
supposed  to  be  equal,  whether  they  are  large  or  small,  this 
being  the  case  when  no  calculation  is  made  for  the  resistance 
of  the  air.     Consequently,  the  weight  of  a  quarter  of  an 
ounce  placed  on  the  large  weight  A,  is  a  representative  of 
all  other  solid  descending  bodies.     The  slowness  of  its  de- 
scent, when  compared  with  freely  gravitating  bodies,  is  only 
a  convenience  by  which  its  motion  can  be  accurately  mea- 
sured, for  it  is  the  increase  of  velocity  which  the  machine 
is  designed  to  ascertain,  and  not  the  actual  velocity  of  falling 
bodies. 

97.  Now  it  will  be  readily  comprehended,  that  in  this 
respect,  it  makes  no  difference  how  slowly  a  body  falls,  pro- 
vided it  follows  the  same  laws  as  other  descending  bodies, 
and  it  has  already  been  stated,  that  all  estimates  on  this  sub- 
ject are  made  from  the  known  distance  a  body  descends 
during  the  first  second  of  time. 

98.  It  follows,  therefore,  that  if  it  can  be  ascertained,  ex- 
actly, how  much  faster  a  body  falls  during  the  third,  fourth, 
or  fifth  second,  than  it  did  during  the  first  second,  by  know- 
ing how  far  it  fell  during  the  first  second,  we  should  be  able 
to  estimate  the  distance  it  would  fall  during  all  succeeding 
seconds. 

99.  If,  then,  by  means  of  a  pendulum  beating  seconds, 
the  weight  A  should  be  found  to  descend  a  certain  number 
of  inches  during  the  first  second,  and  another  certain  number 
during  the  next  second,  and  so  on,  the  ratio  of  increased 
descent  would  be  precisely  ascertained,  and  could  be  easily 

After  the  small  weight  is  taken  off  by  the  ring,  why  does  the  large 
weight  continue  to  descend  7  Does  this  machine  show  the  actual  ve- 
locity of  a  falling  body,  or  only  its  increase  1 

3* 


30  GRAVITY. 

applied  to  the  falling  of  other  bodies;  and  this  is  the  use  to 
which  this  instrument  is  applied. 

100.  By  this  machine,  it  can  also  be  ascertained  how 
much  the  actual  velocity  of  a  falling  body  depends  on  the 
force  of  gravity,  and  how  much  on  acquired  velocity,  for 
the  force  of  gravity  gives  motion  to  the  descending  weight 
only  until  it  arrives  at  the  ring,  after  which  the  motion  is 
continued  by  the  velocity  it  had  before  acquired. 

101.  From  experiments  accurately  made  with  this  ma- 
chine, it  has  been  fully  established,  that  if  the  time  of  a 
falling  body  be  divided  into  equal  parts,  say  into  seconds, 
the  spaces  through  which  it  falls  in  each  second,  taken  se- 
parately, will  be  as  the  odd  numbers,  1,  3,  5,  7,  9,  and  so 
on,  as  already  stated.     To  make   this  plain,  suppose  the 
times  occupied  by  the  falling  body  to  be  1,  2,  3,  and  4  se- 
conds ;  then  the  spaces  fallen  through  will  be  as  the  squares 
of  these  seconds,  or  times,  viz.  1,  4,  9,  and  16,  the  square  of 
1  being  1,  the  square  of  2  being  4,  the  square  of  3,  9,  and 
so  on.     The  distance  fallen  through,  therefore,  during  the 
second  second,  may  be  found,  by  taking  1,  the  distance  cor- 
responding to  one  second,  from  4,  the  distance  corresponding 
to  2  seconds,  and  is  therefore  3.     For  the  third  second,  takr* 
4  from  9,  and  therefore  the  distance  will  be  5.     For  th*i 
fourth  second,  take  9  from  16,  and  the  distance  will  be  7 
and  so  on.     During  the  first  second,  then,  the  body  falls  » 
certain  distance;  during  the  next  second,  it  falls  three  timev 
that  distance ;  during  the  third,  five  times  the  distance  ;  dur 
ing  the  fourth,  seven  times  that  distance,  and  so  continualh 
in  that  proportion. 

102.  It  will  be  readily  conceived,  that  solid  bodies  fall 
ing  from  great  heights,  must  ultimately  acquire  an  amazing 
velocity  by  this  proportion  of  increase.     An  ounce  ball  ot 
lead,  let  fall  from  a  certain  height  towards  the  earth,  woul<? 
thus  acquire  a  force  ten  or  twenty  times  as  great  as  whe» 
shot  out  of  a  rifle.     By  actual  calculation,  it  has  been  found 
that  were  the  moon  to  lose  her  projectile  force,  which  coun- 

How  does  Mr.  Atwood's  machine  show  how  much  the  celei'ity  of  t 
body  depends  upon  gravity,  and  how  much  on  acquired  velocity  \ 
Suppose  the  times  of  a  falling  body  are  as  the  numbers  1,  2,  3,  4,  what 
will  be  the  numbers  representing  the  spaces  through  which  it  falls  1 
Suppose  a  body  falls  16  feet  the  first  second,  how  far  will  it  fall  the 
third  second  1  Would  it  be  possible  for  a  rifle  ball  to  acquire  a  greater 
force  by  falling,  than  if  shot  from  a  rifle  1  How  long  would  it  take 
the  moon  to  come  to  the  earth  according  to  the  law  of  increased 
velocity  ? 


GRAVITY.  3i 

imbalances  the  earth's  attraction,  she  would  fall  to  the  earth 
m  four  days  and  twenty  hours,  a  distance  of  240,000  miles. 
And  were  the  earth's  projectile  force  destroyed,  it  would 
fall  to  the  sun  in  sixty-four  days  and  ten  hours,  a  distance 
of  95,000,000  of  miles. 

103.  Every  one  knows  by  his  own  experience  the  differ- 
ent effects  of  the  same  body  falling  from  a  great  or  a  small 
height.     A  boy  will  toss  up  his  leaden  bullet  and  catch  it 
with  his  hand,  but  he  soon  learns,  by  its  painful  effects,  not 
to  th-row  it  too  high.     The  effects  of  hail-stones  on  window 
glass,  animals,  and  vegetation,  are   often   surprising,  and 
sometimes  calamitous  illustrations  of  the  velocity  of  falling 
bodies. 

104.  It  has  been  already  stated,  that  the  velocities  of  solid 
bodies  falling  from  a  given  height,  towards  the  earth,  are 
equal,  or  in  other  words,  that  an  ounce  ball  of  lead  will  de- 
scend in  the  same  time  as  a  pound  ball  of  lead. 

105.  This  is  true  in  theory,  but  there  is  a  slight  differ- 
ence in  this  respect  in  favour  of  the  velocity  of  the  larger 
body,  owing  to  the  resistance  of  the  atmosphere.     We,  how- 
ever, shall  at  present  consider  all  solids  of  whatever  size, 
as  descending  through  the  same  spaces  in  the  same  times, 
this  being  exactly  true  when  they  pass  without  resistance. 

106.  To  comprehend  the  reason  of  this,  we  have  only  to 
consider,  that  the  attraction  of  gravitation  in  acting  on  a 
mass  of  matter  acts  on  every  particle  it  contains;  and  thus 
every  particle  is  drawn  down  equally  and  with  the  same 
force.     The  effect  of  gravity,  therefore,  is  in  exact  propor- 
tion to  the  quantity  of  matter  the  mass  contains,  and  not  in 
proportion  to  its  bulk.     A  ball  of  lead  of  a  foot  in  diameter, 
and  one  of  wood  of  the  same  diameter,  are  obviously  of  the 
same  bulk;  but  the  lead  will  contain  twelve  particles  of 
matter  where  the  wood  contains  one,  and  consequently  will 
be  attracted  with  twelve  times  the  force,  and  therefore  will 
weigh  twelve  times  as  much. 

107.  Attraction  proportioriable  to  the  quantity  of  mat- 
ter.— If,  then,  bodies  attract  each  other  in  proportion  to  the 
quantities  of  matter  they  contain,  it  follows  that  if  a  mass 

How  long  would  it  take  the  earth  to  fall  to  the  sun  ?  What  fami- 
liar illustrations  are  given  of  the  force  acquired  by  the  velocity  of 
falling  bodies'?  Will  a  small  and  large  body  fall  through  the  same 
space  in  the  same  time  1  On  what  parts  of  a  mass  of  matter  does  the 
force  of  gravity  act!  Is  the  effect  of  gravity  in  proportion  to  bulk,  or 
quantity  of  matter  1 


32  GRAVITY. 

of  the  earth  were  doubled,  the  weights  of  all  bodies  on  its 
surface  would  also  be  doubled ;  and  if  its  quantity  of  matter 
were  tripled,  all  bodies  would  weigh  three  times  as  much 
as  they  do  at  present. 

108.  It  follows  also,  that  two  attracting  bodies,  when  free 
to  move,  must  approach  each  other  mutually.     If  the  two 
bodies  contain  like  quantities  of  matter,  their  approach  will 
be  equally  rapid,  and  they  will  move  equal  distances  towards 
each  other.     But  if  the  one  be  small  and  the  other  large, 
the  small  one  will  approach  the  other  with  a  rapidity  pro- 
portioned to  the  less  quantity  of  matter  it  contains. 

109.  It  is  easy  to  conceive,  that  if  a  man  in  one  boat  pulls 
at  a  rope  attached  to  another  boat,  the  two  boats,  if  of  the 
same  size,  will  move  towards  each  other  at  the  same  rate; 
but  if  the  one  be  large  and  the  other  small,  the  rapidity 
with  which  each  moves  will  be  in  proportion  to  its  size,  the 
large  one  moving  with  as  much  less  velocity  as  its  size  is 
greater. 

110.  A  man  in  a  boat  pulling  a  rope  attached  to  a  ship, 
seems  only  to  move  the  boat,  but  that  he  really  moves  the 
ship  is  certain,  when  it  is  considered,  that  a  thousand  boats 
pulling  in  the  same  manner  would  make  the  ship  meet 
them  half  way. 

111.  It  appears,  therefore,  that  an  equal  force  acting  on 
bodies  containing  different  quantities  of  matter,  move  them 
with  different  velocities,  and  that  these  velocities  are  in  an 
inverse  proportion  to  their  quantities  of  matter. 

112.  In  respect  to  equal  forces,  it  is  obvious  that  in  the 
case  of  the  ship  and  single  boat,  they  were  moved  towards 
each  other  by  the  same  force,  that  is,  the  force  of  a  man 
pulling  by  a  rope.     The  same  principle  holds  in  respect  to 
attraction,  for  all  bodies  attract  each  other  equally,  accord- 
ing to  the  quantities  of  matter  they  contain,  and  since  all  at- 
traction is  mutual,  no  body  attracts  another  with  a  greater 
force  than  that  by  which  it  is  attracted. 

113.  Suppose  a  body  to  be  placed  at  a  distance  from  the 
earth,  weighing  two  hundred  pounds;  the  earth  would  then 
attract  the  body  with  a  force  equal  to  two  hundred  pounds, 

Were  the  mass  of  the  earth  doubled,  how  much  more  should  we 
weigh  than  we  do  now  7  Suppose  one  body  moving  towards  another, 
three  times  as  large,  by  the  force  of  gravity,  what  would  be  their  pro- 
portional velocities'?  How  is  this  illustrated'?  Does  a  large  body  at- 
tract a  small  one  with  any  more  force  than  it  is  attracted  1  Suppose  a 
body  weighing  200  pounds  to  be  placed  at  a  distance  from  the  earth, 
with  how  much  force  does  the  earth  attract  the  body  1 


GRAVITY.  3; 

and  the  body  would  attract  the  earth  with  an  equal  force, 
otherwise  their  attraction  would  not  be  equal  and  mutual. 
Another  body  weighing  ten  pounds,  would  be  attracted  with 
a  force  equal  to  ten  pounds,  and  so  of  all  bodies  according 
to  the  quantity  of  matter  they  contain ;  each  body  being  at- 
tracted by  the  earth  with  a  force  equal  to  its  own  weight, 
and  attracting  the  earth  with  an  equal  force. 

114.  If,  for  example,  two  boats  be  connected  by  a  rope, 
and  a  man  in  one  of  them  pulls  with  a  force  equal  to  100 
pounds,  it  is  plain  that  the  force  on  each  vessel  would  be 
100  pounds.     For,  if  the  rope  were  thrown  over  a  pulley, 
and  a  man  were  to  pull  at  one  end  with  a  force  of  100  pounds, 
it  is  plain  it  would  take  1 00  pounds  at  the  other  end  to  balance. 

115.  Attracting  bodies  approach  each  other. — It  is  in- 
ferred from  the  above    principles,  that  all    attracting  bo- 
dies which  are  free  to  move,  mutually  approach  each  other, 
and  therefore  that  the  earth    moves  towards  every  body 
which  is  raised  from  its  surface,  with  a  velocity  and  to  a 
distance  proportional  to  the  quantity  of  matter  thus  elevated 
from  its  surface.     But  the  velocity  of  the  earth  being  as 
many  times  less  than  that  of  the  falling  body  as  its  mass  is 
greater,  it  follows  that  its  motion  is  not  perceptible  to  us. 

116.  The  following  calculation  will  show  what  an  im- 
mense mass  of  matter  it  would  take,  to  disturb  the  earth's 
gravity  in  a  perceptible  manner. 

117.  If  a  ball  of  earth  equal  in  diameter  to  the  tenth  part 
of  a  mile,  were  placed  at  the  distance  of  the  tenth  part  of  a 
mile  from  the  earth's  surface,  the  attracting  powers  of  the 
two  bodies  would  be  in  the  ratio  of  about  512  millions  of 
millions  to  one.     For  the  earth's  diameter  being  about  8000 
miles,  the  two  bodies  would  bear  to  each  other  about  this 
proportion.     Consequently,  if  the  tenth  part  of  a  mile  were 
divided  into  512  millions  of  millions  of  equal  parts,  one  of 
these  parts  would  be  nearly  the  space  through  which  the 
earth  would  move  towards  the  falling  body.     Now,  in  the 
tenth  part  of  a  mile  there  are  about  6400  inches,  conse- 


With  what  force  does  the  body  attract  the  earth  1  Suppose  a  man  in 
one  boat,  pulls  with  a  force  of  100  pounds  at  a  rope  fastened  to  another 
boat,  what  would  be  the  force  on  each  boat  1  How  is  this  illustrated  ^ 
Suppose  the  body  falls  towards  the  earth,  is  the  earth  set  in  motion  by 
its  attraction  1  Why  is  not  the  earth's  motion  towards  it  perceptible  1 
What  distance  would  a  body,  the  tenth  part  of  a  mile  in  diameter, 
placed  at  the  distance  of  a  tenth  part  of  a  mile,  attract  the  earth  to- 
wards it  1 


34  ASCENT  OF  BODIES. 

quently  this  number  must  be  divided  into  512  millions  of 
millions  of  parts,  which  would  give  the  eighty  thousand 
millionth  part  of  an  inch  through  which  the  earth  would 
move  to  meet  a  body  the  tenth  part  of  a  mile  in  diameter. 

ASCENT  OF  BODIES. 

•  118.  Having  now  explained  and  illustrated  the  influence 
of  gravity  on  bodies  moving  downward  and  horizontally,  it 
remains  to  show  how  matter  is  influenced  by  the  same 
power  when  bodies  are  moved  upward,  or  contrary  to  the 
force  of  gravity. 

What  has  been  stated  in  respect  to  the  velocity  of 
falling  bodies  is  exactly  reversed  in  respect  to  those 
which  are  thrown  upwards,  for  as  the  motion  of  a 
falling  body  is  increased  by  the  action  of  gravity,  so  » 
is  it  retarded  by  the  same  force  when  thrown  up- 
wards. 

A  bullet  shot  upwards,  every  instant  loses  a  part 
of  its  velocity,  until  having  arrived  at  the  highest 
point  from  whence  it  was  thrown,  it  then  returns 
again  to  the  earth. 

The  same  law  that  governs  a  descending  body, 
governs  an  ascending  one,  only  that  their  motions    7 
are  reversed. 

The  same  ratio  is  observed  to  whatever  distance 
the  ball  is  propelled,  or  as  the  height  to  which  it  is 
thrown  may  be  estimated  from  the  space  it  passes 
through  during  the  first  second,  so  its  returning  ve- 
locity is  in  a  like  ratio  to  the  height  to  which  it  was 
sent. 

This  will  be  understood  by  fig.  6.  Suppose  a 
ball  to  be  propelled  from  the  point  a,  with  a  force 
which  would  carry  it  to  the  point  b  in  the  first  se- 
cond, to  c  in  the  next,  and  to  d  in  the  third  second. 
It  would  then  remain  nearly  stationary  for  an  in- 
stant, and  in  returning,  would  pass  through  exactly 
the  same  spaces  in  the  same  times,  onlyvthat  its  di- 
rection would  be  reversed.  Thus  it  will  fall  from 
d  to  c,  in  the  first  second,  to  b  in  the  next,  and  to  a 
in  the  third. 

Now  the  force  of  a  moving  body  is  as  its  velocity  CL 

What  effect  does  the  force  of  gravity  have  on  bodies  moving  up- 
ward 1  Are  upward  and  downward  motion  governed  by  the  saro* 
laws  7  Explain  fig.  6. 


FALLING  BODIES.  55 

and  its  quantity  of  matter,  and  hence  the  same  ball  will  fall 
with  exactly  the  same  force  that  it  rises.  For  instance,  a 
ball  shot  out  of  a  rifle,  with  a  force  sufficient  to  overcome  a 
certain  impediment,  on  returning,  would  again  overcome 
*he  same  impediment. 

FALL  OF  LIGHT  BODIES. 

119.  It  has  been  stated  that  the  earth's  attraction  acts 
equally  on  all  bodies,  containing  equal  quantities  of  matter, 
and  that  in  vacuo,  all  bodies,  whether  large  or  small,  de- 
scend from  the  same  heights  in  the  same  time. 

120.  There  is,  however,  a  great  difference  in  the  quanti- 
ties of  matter  which  bodies  of  the  same  bulk  contain,  and 
consequently  a  difference,  in  the  resistance  which  they  meet 
with  in  passing  through  the  air. 

121.  Now,  the  fall  of  a  body  containing  a  large  quantity 
of  matter  in  a  small  bulk,  meets  with  little  comparative  re- 
sistance, while  the   fall  of  another,  containing   the   same 
quantity  of  matter,  but  of  larger  size,  meets  with  more  in 
comparison,  for  it  is  easy  to  see  that  two  bodies  of  the  same 
size  meet  with  exactly  the  same  actual  resistance.     Thus,  if 
we  let  fall  a  ball  of  lead,  and  another  of  cork,  of  two  inches 
m  diameter  each,  the  lead  will  reach  the  ground  before  the 
cork,  because,  though  meeting  with  the  same  resistance, 
the  lead  has  the  greatest  power  of  overcoming  it. 

122.  This,  however,  does  not  affect  the  truth  of  the  ge- 
neral law  already  established,  that  the  weights  of  bodies 
are  as  the  quantities  of  matter  they  contain.     It  only  shows 
that  the  pressure  of   the  atmosphere  prevents    bulky  and 
porous  substances  from  falling  with  the  same  velocity  as 
those  which  are  compact  or  dense. 

123.  Were  the  atmosphere  removed,  all  bodies,  whether 
light  or  heavy,  large  or  small,  would  descend  with  the  same 
velocity.     This  fact  has  been  ascertained  by  experiment  in 
the  following  manner  : 

124.  The  air  pump  is  an  instrument,  by  means  of  which 
the  air  can  be  pumped  out  of  a  close  vessel,  as  will  be  seen 
under  the  article  Pneumatics.     Taking  this  for  granted  at 
present,  the  experiment  is  made  in  the  following  manner : 

What  is  the  difference  between  the  upward  and  returning  velocity 
of  the  same  body  1  Why  will  not  a  sack  of  feathers  and  a  stone  of  the 
same  size  fall  through  the  air  in  the  same  time  1  Does  this  affect  the  truth 
of  the  general  law,  that  the  weights  of  bodies  are  as  their  quantities  of 
matter  7  What  would  be  the  effect  on  the  fall  of  light  and  heavy  bo- 
dies, were  the  atmosphere  removed  1 


MOTION. 


125.  On  the  plate  of  the  air  pump  A, 
place  the  tall  jar  B,  which  is  open  at  the 
bottom,  and  has  a  brass  cover  fitted  closely 
to  the  top.     Through  the  cover  let  a  wire 
pass,  air  tight,  having  a  small  cross  at  the 
lower  end.      On  each  side  of  this  cross, 
place  a  little  stage,  and  so  contrive  them 
that  hy  turning  the  wire  by  the  handle  C, 
these  stages  shall  be  upset.     On  one  of  the 
stages  place  a  guinea  or  any  other  heavy 
body,  and  on  the  other  place  a  feather. 
When  this  is  arranged,  let  the  air  be  ex- 
hausted from  the  jar  by  the  pump,  and  then 
turn  the  handle  C,  so  that  the  guinea  and 
feather  may  fall  from  their  places,  and  it 
will  be  found  that  they  will  both  strike  the 
plate  at  the  same  instant.     Thus  is  it  de- 
monstrated, that  were  it  not  for  the  resist- 
ance of  the  atmosphere,  a  bag  of  feathers 
and  one  of  guineas  would  fall  from  a  given 
height  with  the  same  velocity  and  in  the 
same  time. 

MOTION. 

126.  Motion  maybe  defined,  a  continued  change  of  place 
with  regard  to  a  fixed  point. 

127.  Without  motion  there  would  be  no  rising  or  setting 
ot  the  sun — no  change  of  seasons — no  fall  of  rain — no  build- 
ing of  houses,  and  finally  no  animal  life.     Nothing  can  be 
done  without  motion,  and  therefore  without  it,  the  whole 
universe  would  be  at  rest  and  dead. 

128.  In  the  language  of  philosophy,  the  power  which 
puts  a  body  in  motion,  is  called  force.     Thus  it  is  the  force 
of  gravity  that  overcomes  the  inertia  of  bodies,  and  draws 
them  towards  the  earth.  The  force  of  water  and  steam  gives 
motion  to  machinery,  &c. 

129.  For  the  sake  of  convenience,  and  accuracy  in  the 
application  of  terms,  motion  is  divided  into  two  kino's,  viz. : 
absolute  and  relative. 

How  is  it  proved  that  a  feather  and  a  guinea  will  fall  through  equal 
spaces  in  the  same  time,  where  there  is  no  resistance  1  How  will  you 
define  motion  1  What  would  be  the  consequence,  were  all  motion  to 
cease  1  What  is  that  power  called  which  puts  a  body  in  motion  1 
How  is  motion  divided  7 


VELOCITY  OP  MOTION.  37 

130.  Absolute  motion  is  a  change  of  place  with  regard  to 
a  fixed  point,  and  is  estimated  without  reference  to  the  mo- 
tion of  any  other  body.     When  a  man  rides  along  the  street, 
or  when  a  vessel  sails  through  the  water,  they  are  both  in 
absolute  motion. 

131.  Relative  motion,  is  a  change  of  place  in  a  body, 
with  respect  to  another  body,  also  in  motion,  and  is  esti- 
mated from  that  other  body,  exactly  as  absolute  motion  is 
from  a  fixed  point. 

132.  The  absolute  velocity  of  the  earth  in  its  orbit  from 
west  to  east,  is  68,000  miles  in  an  hour ;  that  of  Mars,  in 
the  same  direction,  is  55,000  miles  per  hour.     The  earth's 
relative  velocity,  in  this  case,  is  13,000  miles  per  hour  from 
west  to  east.     That  of  Mars,  comparatively,  is  13,000  miles 
from  east  to  west,  because  the  earth  leaves  Mars  that  dis- 
tance behind  her,  as  she  would  leave  a  fixed  point. 

133.  Rest,  in  the  common  meaning  of  the  term,  is  the 
opposite  of  motion,  but  it  is  obvious,  that  rest  is  often  a  rela- 
tive term,  since  an  object  may  be  perfectly  at  rest  with 
respect  to  some  things,  and  in  rapid  motion  in  respect  to 
others.     Thus,  a  man  sitting  on  the  deck  of  a  steam-boat, 
may  move  at  the  rate  of  fifteen  miles  an  hour,  with  respect 
to  the  land,  and  still  be  at  rest  with  respect  to  the  boat.  And 
so,  if  another  man  was  running  on  the  deck  of  the  same  boat 
at  the  rate  of  fifteen  miles  the  hour  in  a  contrary  direction, 
he  would  be  stationary  in  respect  to  a  fixed  point,  and  still 
be  running  with  all  his  might,  with  respect  to  the  boat. 

VELOCITY  OF  MOTION. 

134.  Velocity  is  the  rate  of  motion  at  which  a  body 
moves  from  one  place  to  another. 

135.  Velocity  is  independent  of  the  weight  or  magnitude 
of  the  moving  body.     Thus  a  cannon  ball  and  a  musket 
ball,  both  flying  at  the  rate  of  a  thousand  feet  in  a  second, 
have  the  same  velocities. 

136.  Velocity  is  said  to  be  uniform,  when  the  moving 
body  passes  over  equal  spaces  in  equal  times.     If  a  steam- 
boat moves  at  the  rate  often  miles  every  hour,  her  velocity 
is  uniform.      The  revolution  of  the  earth  from  west  to  east 
is  a  perpetual  example  of  uniform  motion. 

What  is  absolute  motion  7     What  is  relative  motion  7     What  is  the 
earth's  relative  velocity  in  respect  to  Mars  1     In  what  respect  is  amtui 
in  a  steam-boat  at  rest,  and  in  what  respect  does  he  move  1     What  is 
velocity  ?     When  is  velocity  uniform  ? 
4 


38  MOMENTUM. 

137.  Velocity  is  accelerated,  when  the  rate  of  motion  is 
constantly  increased,  and  the  moving  body  passes  through 
unequal  spaces  in  equal  times.     Thus,  when  a  falling  body 
?noves  sixteen  feet  during  the  first  second,  and  forty-eight 
feet  during  the  next  second,  and  so  on,  its  velocity  is  accele- 
rated.    A  body  falling  from  a  height  freely  through  the  air, 
is  the  most  perfect  example  of  this  kind  of  velocity. 

138.  Retarded  velocity,  is  when  the  rate  of  motion  of  the 
oody  is  constantly  decreased,  and  it  is  made  to  move  slower 
and  slower.      A  ball  thrown  upwards  into  the  air,  has  its 
velocity  constantly  retarded  by  the  attraction  of  gravitation, 
and  consequently,  it  moves  slower  every  moment. 

FORCE,  OR  MOMENTUM  OF  MOVING  BODIES. 

139.  The  velocities  of  bodies  are  equal,  when  they  pass 
over  equal  spaces  in  the  same  time ;  but  the  force   with 
which  bodies,  moving  at  the  same  rate,  overcome  impedi- 
ments, is  in  proportion  to  tbe  quantity  of  matter  they  contain. 
This  power,  or  force,  is  called  the  momentum  of  the  moving 
body. 

140.  Thus,  if  two  bodies  of  the  same  weight  move  with 
the  same  velocity,  their  momenta  will  be  equal. 

141.  Two  vessels,  each  of  a  hundred  tons,  sailing  at  the 
rate  of  six  miles  an  hour,  would  overcome  the  same  impedi- 
ments, or  be  stopped  by  the  same  obstructions.     Their  mo- 
menta would  therefore  be  the  same. 

142.  The  force,  or  momentum  of  a  moving  body,  is  in 
proportion  to  its  quantity  of  matter,  and  its  velocity. 

143.  A  large  body  moving  slowly,  may  have  less  mo- 
mentum than  a  small  one  moving  rapidly.     Thus,  a  bullet, 
shot  out  of  a  gun,  moves  with  much  greater  force  than  a 
stone  thrown  by  the  hand.     The  momentum  of  a  body  is 
found  by  multiplying  its  quantity  of  matter  by  its  velocity. 

144.  Thus,  if  the  velocity  be  2,  and  the  weight  2,  the  mo- 
mentum will  be  4.     If  the  velocity  be  6,  and  the  weight  of 
the  body  4,  the  momentum  will  be  24. 

145.  If  a  moving  body  strikes  an  impediment,  the  forco 
tvith  which  it  strikes,  and  the  resistance  of  the  impediment, 

When  is  velocity  accelerated  1  Give  illustrations  of  these  two  kinds 
of  velocity.  What  is  meant  by  retarded  velocity  1  Give  an  example 
of  retarded  velocity.  What  is  meant  by  the  monr.entum  of  a  body  1 
When  will  the  momenta  of  two  bodies  be  equal  1  Give  an  example. 
When  has  a  small  body  more  momentum  than  a  large  one  1  By  what 
rule  is  the  momentum  of  a  body  found  1 


MOMENTUM. 


39 


are  equal.  Thus,  if  a  boy  throw  his  ball  against  the  side 
of  the  house,  with  the  force  of  3,  the  house  resists  it  with 
an  equal  force,  and  the  ball  rebounds  If  he  throvvs  it 
against  a  pane  of  glass  with  the  same  force,  the  glass  hav- 
ing only  the  power  of  2  to  resist,  the  ball  will  go  through 
the  glass,  still  retaining  one  third  of  its  force. 

146.  Action  and  re-action  equal.  —  From  observations 
made  on  the  effects  of  bodies  striking  each  other,  it  is  found 
that  action  and  re-action  are  equal  ;  or,  in  other  words,  that 
force  and  resistance  are  equal.     Thus,  when  a  moving  body 
strikes  one  that  is  at  rest,  the  body  at  rest  returns  the  blow 
with  equal  force. 

This  is  illustrated  by  the  well  known  fact,  that  if  two 
persons  strike  their  heads  together,  one  being  in  motion, 
and  the  other  at  rest,  they  are  both  equally  hurt. 

147.  The  philosophy  of  action  and  re-action  is  finely  illus- 
trated by  a  number  of  ivory  balls,  suspended  by  threads,  as 
in  fig.  10,  so  as  to  touch  each  Fig.  10. 

other.     If  the  ball  a  be  drawn 

from    the    perpendicular,   and 

then  let  fall,  so  as  to  strike  the 

one  next  to  it,  the  motion  of  the 

falling  ball  will  be  communi- 

cated through  the  whole  series, 

from  one  to  the  other.  None  of 

the  balls,  except  /,  will,  how- 

ever,  appear   to  move.     This 

will  be  understood,  when  we 

consider  that  the  re-action  of  b, 

is  just  equal  to  the  action  of  a, 

and  that  each  of  the  other  balls, 

in  like  manner,  acts,  and  re-  / 

acts,  on  the  other,  until  the  mo- 

tion of  a  arrives  at  /  which,  having  no  impediment,  or 

nothing  to  act  upon,  is  itself  put  in  motion.     It  is,  therefore, 

re-action,  which  causes  all  the  balls,  except  /  to  remain  at 

rest. 

148.  It  is  by  a  modification  of  the  same  principle,  that 
rockets  are  impelled  through  the  air.  The  stream  of  ex- 
panded air,  or  the  fire,  which  is  emitted  from  the  lower  end 

When  a  moving:  body  strikes  an  impediment,  which  receives  the 
greatest  shock  1  What  is  the  law  of  action  and  re-action  ?  How  is 
this  illustrated  1  When  one  of  the  ivory  balls  strikes  the  other,  why 
does  the  most  distant  one  only  move  3 


e  d   C  b 


40  REFLECTED  MOTION. 

of  the  rocket,  not  only  pushes  against  the  rocket  itself,  but 
against  the  atmospheric  air,  which,  re-acting  against  the  air 
so  expanded,  sends  the  rocket  along. 

149.  It  was  on  account  of  not  understanding  the  princi- 
ples of  action  and  re-action,  that  the  man  undertook  to  make 
a  fair  wind  for  his  pleasure  boat,  to  be  used  whenever  he 
wished  to  sail.     He  fixed  an  immense  bellows  in  the  stern 
of  his  boat,  not  doubting  but  the  wind  from  it  would  carry 
him  along.     But  on  making  the  experiment,  he  found  that 
his  boat  went  backwards  instead  of  forwards.     The  reason 
is  plain.     The  re-action  of  the  atmosphere  on  the  stream  of 
wind  from  the  bellows,  before  it  reached  the  sail,  moved 
the  boat  in  a  contrary  direction.     Had  the  sails  received  the 
whole  force  of  the  wind  from  the  bellows,  the  boat  would  not 
have  moved  at  all,  for  then,  action  and  re-action  would  have 
been  exactly  equal,  and  it  would  have  been  like  a  man's  at- 
tempting to  raise  himself  over  a  fence  by  the  straps  of  his 
boots. 

REFLECTED  MOTION. 

150.  It  has  been  stated  that  all  bodies,  when  once  set  in 
motion,  would  continue  to  move  straight  forward,  until  some 
impediment,  acting  in   a  contrary  direction,  should  bring 
them  to  rest ;  continued  motion  without  impediment  being  a 
consequence  of  the  inertia  of  matter. 

151.  Such  bodies  are  supposed  to  be  acted  upon  by  a  sin- 
gle force,  and  that  in  the  direction  of  the  line  in  which  they 
move.     Thus,  a  ball  sent  out  of  a  gun,  or  struck  by  a  bat, 
turns  neither  to  the  right  nor  left,  but  makes  a  curve  to- 
wards the  earth,  in  consequence  of  another  force,  which  is 
the  attraction  of  gravitation,  and  by  which,  together  with 
the  resistance  of  the  atmosphere,  it  is  finally  brought  to  the 
ground. 

152.  The  kind  of  motion  now  to  be  considered,  is  thav 
which  is  produced  when  bodies  are  turned  out  of  a  straighi 
line  by  some  force,  independent  of  gravity. 

153.  A  single  force,  or  impulse,  sends  the  body  directly 
forward,  but  another  force,  not  exactly  coinciding  with  this 
will  give  it  a  new  direction,  and  bend  it  out  of  its  former 
course. 

On  what  principle  are  rockets  impelled  through  the  air  1  In  the  ex 
periment  with  the  boat  and  bellows,  why  did  the  boat  move  back 
wards  1  Why  would  it  not  have  moved  at  all,  had  the  sail  receive** 
all  the  wind  from  the  bellows  1  Suppose  a  body  is  acted  on,  and  s* 
wi  motion  by  a  single  force,  in  what  direction  will  it  move  ? 


REFLECTED  MOTION. 


41 


154.  If;  for  instance,  two  moving  bodies  strike  each  other 
obliquely,  they  will  both  be  thrown  out  of  the  line  of  their 
former  direction.      This  is  called  reflected  motion,  because 
it  observes  the  same  laws  as  reflected  light. 

155.  The  bounding  of  a  ball;  the  skipping  of  a  stone 
over  the  smooth  surface  of  a  pond ;  and  the  oblique  direction 
of  an  apple,  when  it  touches  a  limb  in  its  fall,  are  examples 
"A  reflected  motion. 

156.  By  experiments  on  this  kind  of  motion,  it  is  found, 
that  moving  bodies  observe  certain  laws,  in  respect  to  the  di- 
rection they  take  in  rebounding  from  any  impediment  they 
happen  to  strike.    Thus,  a  ball,  striking  on  the  floor,  or  wall 
of  a  room,  makes  the  same  angle  in  leaving  the  point  where 
it  strikes,  that  it  does  in  approaching  it. 

157.  Suppose  a  b, 

fig.  11,  to  be  a  marble  Fig.  11. 

slab,  or  floor,  and  c  to 
be  an  ivory  ball,  which 
has  been  thrown  to- 
wards the  floor  in  the 

direction  of  the  line  c     r   ^^  ^ 

c  ;  it  will  rebound  in  lL~ 

the  direction  of  the  line  e  d,  thus  making  the  two  angles 

/and  g  exactly  equal. 

158.  If  the  ball  approached  the  floor  under  a  larger  or 
smaller  angle,  its  rebound  would  observe  the  same  rule. 
Thus,  if  it  fell  in  the  Fig.  13. 

line  h  k,  fig.  12,  its  re- 
bound would  be  in  the  £-  £  Jt, 
line  k  i,  and  if  it  was 
dropped  perpendicu- 
larly from  I  to  &,  it 
would  return  in  the 
same  line  to  I.  The  an- 
gle which  the  ball 
makes  with  the  per- 
pendicular I  k,  in  its 
approach  to  the  floor,  is  called  the  angle  of  incidence,  and 

What  is  the  motion  called,  when  a  body  is  turned  out  of  a  straight 
line  by  another  force  1  What  illustrations  can  you  give  of  reflected 
motion  1  What  laws  are  observed  in  reflected  motion  1  Suppose  a  ball 
to  be  thrown  on  the  floor  in  a  certain  direction,  what  rule  will  it  ob- 
serve in  rebounding  1  What  is  the  angle  called,  which  the  ball  make* 
in  approaching  the  floor  7 


d     Fig.  13. 


COMPOUND  MOTION. 

that  which  it  makes  in  departing  from  the  floor  in  ihe  same 
line,  is  called  the  angle  of  reflection,  and  these  angles  are 
always  equal  to  each  other. 

COMPOUND  MOTION. 

159.  Compound  motion  is  that  motion  which  is  produced 
by  two  or  more  forces,  acting  in  different  directions,  on  the 
same  body,  at  the  same  time.     This  will  be  readily  unuer- 
stood  by  a  diagram. 

160.  Suppose  the  ball  a, 
fig.  13,  to  be  moving  with 
a  certain  velocity  in   the 
line  b  c,  and  suppose  that 
at  the  instant  when  it  came  b~ 
to  the  point  a,  it  should  be 
struck  with  an  equal  force 
in  the  direction  of  d  e,  as 

it  cannot  obey  the  direction 
of  both  these  forces,  it  will 
take  a  course  between 
them,  and  fly  off  in  the  di- 
rection of  /. 

161.  The  reason  of  this 

is  plain.  The  first  force  would  carry  the  ball  from  b  to  c  ; 
the  second  would  carry  it  from  d  to  e ;  and  these  two  forces 
being  equal,  gives  it  a  direction  just  half  way  between  the 
two,  and  therefore  it  is  sent  towards/ 

162.  The  line  a  f,  is  called  -the  diagonal  of  the  square, 
and  results  from  the  cross  forces,  b  and  d,  being  equal  to  each 
other.     If  one  of  the  moving  forces  is  greater  than  the 
other,  then  the  diagonal  line  will  be  lengthened  in  the  di- 
rection of  the  greater  force,  and  instead  of  being  the  diago- 
nal of  a  square,  it  will  become  the  diagonal  of  a  parallelo- 
gram, or  oblong  square. 

What  is  the  angle  called,  which  it  makes  in  leaving  the  floor?  What 
is  the  difference  between  these  angles  1  What  is  compound  motion  ? 
Suppose  a  ball,  moving  with  a  certain  force,  to  be  struck  crosswise 
with  the  same  force,  in  what  direction  will  it  move  1 


CIRCULAR  MOTION.  43 

163.  Suppose  the  force  tfig.  14. 
'.n   the  direction  of  a  bt 

should  drive  the  ball  with 

twice  the  velocity  of  the  ° 

cross  force    c  d,  fig.  14, 

then  the  ball    would   go 

twice  as  far  from  the  line 

c  d,  as  from  the  line  b  a, 

and  ef  would  be  the  di-   - 

agonal  of  a  parallelogram  - 

whose  length  is  double  its  breadth. 

164.  Suppose  a  boat,  in  crossing  a  river,  is  rowed  forward 
at  the  rate  of  four  miles  an  hour,  and  the  current  of  the  river 
is  at  the  same  rate,  then  the  two  cross  forces  will  be  equal, 
and  the  line  of  the  boat  will  be  the  diagonal  of  a  square,  as 
in  fig.  13.     But  if  the  current  be  four  miles  an  hour,  and 
the  progress  of  the  boat  forward  only  two  miles  an  hour, 
then  the  boat  will  go  down  stream  twice  as  fast  as  she  goes 
across  the  river,  and  her  path  will  be  the  diagonal  of  a  pa- 
rallelogram, as  in  fig.  14,  and  therefore  to  make  the  boat 
pass  directly  across  the  stream,  it  must  be  rowed  towards 
some  point  higher  up  the  stream  than  the  landing  place ;  a 
fact  well  known  to  boatmen. 

CIRCULAR  MOTION. 

165.  Circular  motion  is  the  motion  of  a  body  in  a  ring,  or 
circle,  and  is  produced  by  the  action  of  two  forces.     By  one 
of  these  forces,  the  moving  body  tends  to  fly  off  in  a  straight 
line,  while  by  the  other  it  is  drawn  towards  the  centre,  and 
thus  it  is  made  to  revolve,  or  move  round  in  a  circle. 

166.  The  force  by  which  a  body  tends  to  go  off  in  a 
straight  line,  is  called  the  centrifugal  force ;  that  which 
keeps  it  from  flying  away,  and  draws  it  towards  the  centre, 
is  called  the  centripetal  force. 

167.  Bodies  moving  in  circles  are  constantly  acted  upon 
by  these  two  forces.     If  the  centrifugal  force  should  cease, 
the   moving  body  would  no  longer  perform  a  circle,  but 
would  directly  approach  the  centre  of  its  own  motion.     If 

Suppose  it  to  be  struck  with  half  its  former  force,  in  what  direction 
will  it  move?  What  is  the  line  af,  fig.  13,  called  7  What  is  the  line 
ef,  fig.  14,  called  1  How  are  these  figures  illustrated  1  What  is  circu- 
lar motion  1  How  is  this  motion  produced  1  What  is  the  centrifugal 
forcel  What  is  the  centripetal  force'?  Suppose  the  centrifugal  force 
should  cease,  in  what  direction  would  the  body  move  7 


44      .  CIRCULAR  MOTION. 

the  centripetal  force  should  cease,  the  body  would  instantly 
begin  to  move  off  in  a  straight  line,  this  being,  as  we  have 
explained,  the  direction  which  all  bodies  take  when  acted 
on  by  a  single  force. 

168.  This   will  be  obvious  Fig.  15. 
by  fig.  15.     Suppose  a  to  be  a 

cannon  ball,  tied  with  a  string 
to  the  centre  of  a  slab  of  smooth 
marble,  and  suppose  an  attempt 
be  made  to  push  this  ball  with 
the  hand  in  the  direction  of  b ; 
it  is  obvious  that  the  string, 
would  prevent  its  going  to  that 
point ;  but  would  keep  it  in 
the  circle.  In  this  case,  the 
string  is  the  centripetal  force. 

169.  Now  suppose  the  ball 

to  be  kept  revolving  with  rapidity,  its  velocity  and  weight 
will  occasion  its  centrifugal  force;  and  if  the  string  were 
cut,  when  the  ball  was  at  the  point  c,  for  instance,  this  force 
would  carry  it  off  in  the  line  towards  b. 

170.  The  greater  the  velocity  with  which  a  body  moves 
round  in  a  circle,  the  greater  will  be  the  force  with  which 
it  will  fly  off  in  a  right  line. 

171.  Thus,  when  one  wishes  to  sling  a  stone  to  the  great- 
est distance,  he  makes  it  whirl  round  with  the  greatest  pos- 
sible rapidity,  before  he  lets  it  go.     Before  the  invention  of 
other  warlike  instruments,  soldiers   threw   stones  in  this 
manner,  with  great  force,  and  dreadful  effects. 

172.  The  line  about  which  a  body  revolves,  is  called  its 
axis  of  motion.     The  point   round  which  it  turns,  or  on 
which  it  rests,  is  called  the  centre  of  motion.     In  fig.  15, 
the  point  d,  to  which  the  string  is  fixed,  is  the  centre  of  mo- 
tion.    In  the  spinning  top,  a  line  through  the  centre  of  the 
handle  to  the  point  on  which  it  turns,  is  the  axis  of  motion. 

173.  In  the  revolution  of  a  wheel,  that  part  which  is  at 
the  greatest  distance  from  the  axis  of  motion,  has  the  great- 
est  velocity,   and,    consequently,   the    greatest    centrifugal 
force. 

Suppose  the  centripetal  force  should  cease,  where  would  the  body  go  1 
Explain  fig.  15.  What  constitutes  the  centrifugal  force  of  a  body 
moving  round  in  a  circle?  How  is  this  illustrated?  What  is  the  axis 
of  motion  1  What  is  the  centre  of  motion  1  drive  illustrations.  What 
part  of  a  revolving  wheel  has  the  greatest  centrifugal  force. 


CENTRE  OF  GRAVITY. 


45 


174.  Suppose  the  wheel,  fig.  Fig.  16. 
16,  to  revolve  a  certain  number 

of  times  in  a  minute,  the  velocity 
of  the  end  of  the  arm,  at  the 
point  a,  would  be  as  much  great- 
er than  its  middle  at  the  point  bt 
as  its  distance  is  greater  from  the 
axis  of  motion,  because  it  moves 
in  a  larger  circle,  and  conse- 
quently the  centrifugal  force  of 
the  rim  c,  would,  in  like  manner, 
be  as  its  distance  from  the  centre 
of  motion. 

175.  Large  wheels,  which  are  designed  to  turn  with  great 
velocity,    must,   therefore,   be    made    with    corresponding 
strength,  otherwise  the  centrifugal  force  will  overcome  the 
cohesive  attraction,  or  the  strength  of  the  fastenings,  in  which 
case  the  wheel  will  fly  in  pieces.     This  sometimes  happens 
to  the  large  grindstones  used  in  gun -factories,  and  the  stone 
either  flies  away  piece-meal,  or  breaks  in  the  middle,  to  the 
great  danger  of  the  workmen. 

176.  Were  the  diurnal  velocity  of  the  earth  about  seven- 
teen times  greater  than  it  is,  those  parts  at  the  greatest  dis- 
tance from  its  axis,  would  begin  to  fly  off  in  straight  lines, 
as  the  water  does  from  a  grindstone,  when  it  is  turned  rap- 
idly. 

CENTRE  OF  GRAVITY. 

177.  The  centre  of  gravity,  in  any  body  or  system  of 
bodies,  is  that  point  upon  which  the  body,  or  system  of 
bodies,  acted  upon  only  by  gravity,  will  balance  itself  in  all 
positions. 

178.  The  centre  of  gravity,  in  a  wheel  made  entirely  of 
wood,  and  of  equal  thickness,  would  be  exactly  in  the  mid- 
dle, or  in  its  ordinary  centre  of  motion.     But  if  one  side  of 
the  wheel  were  made  of  iron,  and  the  other  part  of  wood, 
its  centre  of  gravity  would  be  changed  to  some  point,  aside 
from  the  centre  of  the  wheel. 

Why  7  Why  must  large  wheels,  turning  with  great  velocity,  be 
strongly  made'?  What  would  be  the  consequence,  were  the  velocity  of 
the  earth  17  times  greater  than  it  is  1  Where  is  the  centre  of  gravity  in 
a  body  1  Where  is  the  centre  of  gravity  in  a  wheel,  made  of  wood  1 
If  one  side  is  made  of  wood,  and  the  other  of  iron,  where  is  the  centre? 


46 


CENTRE  OF  GRAVITY. 


179.  Thus,  the  centre  ot  gravity  Fig.  17. 
in  the  wooden  wheel,  fig.  17,  would 

be  at  the  axis  on  which  it  turns  ;  but 
were  the  arm  a,  of  iron,  its  centre 
of  motion  and  of  gravity  would  no 
longer  be  the  same,  but  while  the 
centre  of  motion  remained  as  before, 
the  centre  of  gravity  would  fall  to 
the  point  a.  Thus  the  centre  of 
motion  and  of  gravity,  though  often 
at  the  same  point,  are  not  always  so. 

180.  When  the  body  is  shaped  irregularly,  or  there  are 
two  or  more  bodies  connected,  the  centre  of  gravity  is  the 
point  on  which  they  will  balance  without  falling. 

181.  If  the  two  balls,  a  and  b,  fig.  Fig- 13. 

18,  weigh  each  four  pounds,  the  cen- 
tre of  gravity  will  be  a  point  on  the 
bar  equally  distant  from  each. 

182.  But   if  one  of  the   balls  be 
heavier  than  the  other,  then  the  cen- 
tre of  gravity  will,  in  proportion,  ap- 
proach the  larger  ball.     Thus,  in  fig. 

19,  if  c  weighs  two  pounds,  and   d 

eight  pounds,  the  centre  of  gravity  will  be  four  times  the 
distance  from  c  that  it  is  from  d. 

183.  In  a  body  of  equal  thickness,  as  a  board,  or  a  slab 
of  marble,  but  otherwise  of  an  irregular  shape,  the  centre 
of  gravity,  may  be  found  by  suspending  it,  first  from  one 
point,  and  then  from  another,  and  marking,  by  means  of  3 
plumb  line,  the  perpendicular  ranges  from  the  point  of  sus- 
pension.    The  centre  of  gravity  will  be  the  point  where- 
these  two  lines  cross  each  other. 

Thus,  if 
the  irregular 
shaped  piece 
of  board,  fig. 

20,  be    sus- 
pended     by 
making       a 
hole  through 
it  at  the  point 

Is  the  centre  of  motion  and  of  gravity  always  the  same  7  When  twt 
bodies  are  connected,  as  by  a  bar  between  them  where  is  the  centre  of 
gravity  7 


Fig.  20. 


Fig.  21. 


Fig.  22. 


CENTRE  OF  GRAVITY.  47 

a,  and  at  the  same  point  suspending  the  plumb  line  c,  both 
board  and  line  will  hang  in  the  position  represented  in  the 
figure.  Having  marked  this  line  across  the  board,  let  it  be 
suspended  again  in  the  position  of  fig.  21,  and  the  perpen- 
dicular line  again  marked.  The  point  where  these  lines 
cross  each  other  is  the  centre  of  gravity,  as  seen  by  fig.  22. 

184.  It  is  often  of  great  consequence,  in  the  concerns  of 
life,  that  the  subject  of  gravity  should  be  well  considered, 
since  the  strength  of  buildings,  and  of  machinery,  often  de- 
pends chiefly  on  the  gravitating  point: 

185.  Common  experience  teaches,  that  a  tall  object,  with 
a  narrow  base,  or  foundation,  is  easily  overturned ;  but  com- 
mon experience  does  not  teach  the  reason,  for  it  is  only  by 
understanding  principles,  that  practice  improves  experiment. 

186.  An  upright  object  will  fall  to  the  ground,  when  it 
leans  so  much  that  a  perpendicular  line  from  its  centre  of 
gravity  falls  beyond  its  base.     A  tall  chimney,  therefore, 
with  a  narrow  foundation,  such  as  are  commonly  built  at  the 
present  day,  will  fall  with  a  very  slight  inclination. 

187.  Now,  in  falling,  the  centre  of  gravity  passes  through 
the  part  of  a  circle,  the  centre  of  which  is  at  the  extremity 
of  the  base  on  which  the  body  stands.     This  will  be  com- 
prehended by  fig.  23. 

188.  Suppose  the  figure  to  be  a  block 
of  marble,  which  is  to  be  turned  over, 
by  lifting  at  the  corner  a,  the  corner  d 
would  be  the  centre  of  its  motion,  or 
the  point  on  which  it  would  turn.   The 
centre  of  gravity,  c,  would,  therefore, 
describe  the  part  of  a  circle,  of  which    # 
the  corner,  d,  is  the  centre. 

189.  It  will  be  obvious,  after  a  little  consideration,  that 
the  greatest  difficulty  we  should   find  in  turning  over  a 
square  block  of  marble,  would  be,  in  first  raising  up  the  cen- 
tre of  gravity,  for  the  resistance  will  constantly  become  less, 
in  proportion  as  the  point  approaches  a  perpendicular  line 
over  the  corner  d,  which,  having  passed,  it  will  fall  by  its 
own  gravity. 

In  a  board  of  irregular  shape,  by  what  method  is  the  centre  of  grav- 
ity found1?  In  what  direction  must  the  centre  of  gravity  be  from  the 
outside  of  the  base,  before  the  object  will  fall  1  In  falling,  the  centre  of 
gravity  passes  through  part  of  a  circle ;  where  is  the  centre  of  this  cir- 
cle'? In  turning  over  a  body,  why  does  the  force  required  constantly 
become  less  and  less  1 


48  CENTRE  OP  GRAVITY. 

190.  The  difficulty  of  turning  over  a  body  of  a  particular 
form,  will  be  more  strikingly  illustrated  by  the  figure  of  a 
triangle,  or  low  pyramid. 

191.  In  fig.  24,  the  centre  of  gravity  is  Fig.  24. 
so   low,  and  the  base  so  broad,  that  in 

turning  it  over,  a  great  proportion  of  its 
whole  weight  must  be  raised.  Hence  we 
see  the  firmness  of  the  pyramid  in  theo- 
ry, and  experience  proves  its  truth ;  for 
buildings  are  found  to  withstand  the  ef- 
fects of  time,  and  the  commotions  of  earthquakes,  in  propor- 
tion as  they  approach  this  figure. 

The  most  ancient  monuments  of  the  art  of  building,  now 
standing,  the  pyramids  of  Egypt,  are  of  this  form. 

192.  When  a  ball  is  rolled  on  a  horizontal  plane,  the 
centre  of  gravity  is  not  raised,  but  moves  in  a  straight  line 
parallel  to  the  surface  of  the  plane  on  which  it  rolls,  and  is 
consequently  always  directly  over  its  centre  of  motion. 

193.  Suppose,  fig.  25,  a  is  the  Fig.  25. 
plane  on  which  the  ball  moves,  b 

the  line  on  which  the  centre  of 

gravity  moves,  and  c  a  plumb  line, 

showing  that  the  centre  of  gravity 

must  always  be  exactly  over  the 

centre  of  motion,  when  the  ball 

moves  on  a  horizontal  plane — then 

we  shall  see  the  reason  why  a  ball 

moving  on  such  a  plane,  will  rest  with  equal  firmness  in 

any  position,  and  why  so  little  force  is  required  to  set  it  in 

motion.     For  in  no  other  figure  does  the  centre  of  gravity 

describe  a  horizontal  line  over  that  of  motion,  in  whatever 

direction  the  body  is  moved. 

194.  If  the  plane  is  inclined  downwards,  the  ball  is  in- 
stantly thrown  into  motion,  because  the  centre  of  gravity  then 
falls  forward  of  that  of  motion,  or  the  point  on  which  the 
ball  rests. 


Why  is  there  less  force  required  to  overturn  a  cube,  or  square,  than 
a  pyramid  of  the  same  weight  1  When  a  ball  is  rolled  on  a  horizon- 
tal plane,  in  what  direction  does  the  centre  of  gravity  move  1  Explain 
fig.  25.  Why  does  a  ball  on  a  horizontal  plane  rest  equally  well  in  all 
positions'?  Why  does  it  move  with  little  force 7  If  the  plane  is  in- 
«lined  downwards,  why  does  the  ball  roll  in  that  direction  1 


CENTRE  OP  GRAVITY. 


49 


195.  This  is  explained  by  fig.  26,  Fig.  26. 
where  a  is  the  point  on  which   the 

ball  rests,  or  the  centre  of  motion,  c 
the  perpendicular  line  from  the  cen- 
tre of  gravity  as  shown  by  the  plumb 
weight  c. 

If  the  plane  is  inclined  upward, 
force  is  required  to  move  the  ball  in 
that  direction,  because  the  centre  of 
gravity  then  falls  behind  that  of  mo- 
tion, and  therefore  the  centre  of  gravr 
ity  has  to  be  constantly  lifted.  This 
is  also  shown  by  fig.  26,  only  considering  the  ball  to  be 
moving  up  the  inclined  plane,  instead  of  down  it. 

196.  From  these  principles,  it  will  be  readily  understood, 
why  so  much  force  is  required  to  roll  a  heavy  body,  as  a 
hogshead  of  sugar,  for  instance,  up  an  inclined  plane.     The 
centre  of  gravity  falling  behind  that  of  motion,  the  weight  is 
constantly  acting  against  the  force  employed  to  raise  the  body. 

197.  From  what  has  been  stated,  it  will       Fig.  27. 
6e  understood,  that  the  danger  that  a  body 

will  fall,  is  in  proportion  to  the  narrowness 
of  its  base,  compared  with  the  height  of  the 
centre  of  gravity  above  the  base. 

198.  Thus,  a  tall  body,  shaped  like  fig.  27, 
will  fall,  if  it  leans  but  very  slightly,  for  the 
centre  of  gravity  being  far  above  the  base,  at 
a,  is  brought  over  the  centre  of  motion,  b,- 
with  little  inclination,  as  shown  by  the  plumb 
line.     Whereas  a  body  shaped  like  fig.  28, 
will  not  fall  until  it  leans  much  more,  as  again 
shown  by  the  direction  of  the  plumb  line. 

199.  We  may  learn,  from  these  compari- 
sons, that  it  is  more  dangerous  to  ride  in  a 
high  carriage  than  in  a  low  one,  in  propor- 
tion to  the  elevation  of  the  vehicle,  and  the 
nearness  of  the  wheels  to  each  other,  or  in 
proportion  to  the  narrowness  of  the  base,  and 
the  height  of  the  centre  of  gravity.     A  load 

Why  is  force  required  to  move  a  ball  up  an  inclined  plane  1  What  is 
the  danger  that  a  body  will  fall  proportioned  to  1  Why  is  a  body,  shapea 
like  fig.  27,  more  easily  thrown  down,  than  one  shaped  like  fig-  26 1 
Hence,  in  riding  in  a  carriage,  how  is  the  danger  of  upsetting  propor- 
tioned ? 

5 


50  CENTRE  OP  GRAVITY. 

of  hay  upsets  where  the  road  raises  one  wheel  but  little 
higher  than  the  other,  because  it  is  high,  and  broader  on  the 
top  than  the  distance  of  the  wheels  from  each  other;  while 
a  load  of  stone  is  very  rarely  turned  over,  because  the  centre 
of  gravity  is  near  the  earth,  and  its  weight  between  the 
wheels,  instead  of  being  far  above  them. 

200.  In  man  the  centre  of  gravity  is  between  the  hips,  and 
hence,  were  his  feet  tied  together,  and  his  arms  tied  to  his 
sides,  a  very  slight  inclination  of  his  body  would  carry  the 
perpendicular  of  his  centre  of  gravity  beyond  the  base,  and 
he  would  fall.     But  when  his  limbs  are  free  to  move,  he 
widens  his  base,  and  changes  the  centre  of  gravity  at  plea- 
sure, by  throwing  out  his  arms,  as  circumstances  require. 

201.  When  a  man  runs,  he  inclines  forward,  so  that  the 
centre  of  gravity  may  hang  before  his  base,  and  in  this  po- 
sition, he  is  obliged  to  keep  his  feet  constantly  advancing, 
otherwise  he  would  fall  forward. 

202.  A  man  standing  on  one  foot,  cannot  throw  his  body 
forward  without  at  the  same  time  throwing  his  other  foot 
backward,  in  order  to  keep  his  centre  of  gravity  within  the 
base. 

203.  A  man,  therefore,  standing  with  his  heels  against  a 
perpendicular  wall,  cannot  stoop  forward  without  falling,  be- 
cause the  wall  prevents  his  throwing  any  part  of  his  body 
backward.     A  person  little  versed  in  such  things,  agreed  to 
pay  a  certain  sum  of  money  for  an  opportunity  of  possessing 
himself  of  double  the  sum,  by  taking  it  from  the  floor  with 
his  heels  against  the  wall.      The  man,  of  course,  lost  his 
money,  for  in  such  a  posture,  one. can  hardly  reach  lower 
than  his  own  knee. 

204.  The  base,  on  which  a  man  is  supported,  in  walking 
or  standing,  is  his  feet,  and  the  space  between  them.     By 
turning  the  toes  out,  this  base  is  made  broader,  without 
taking  much  from  its  length,  and  hence  persons  who  turn 
their  toes  outward,  not  only  walk  more  firmly,  but  more 
gracefully,  than  those  who  turn  them  inward. 

205.  In  consequence  of  the  upright  ppsition  of  man,  he  is 
constantly  obliged  to  employ  some  exertion  to  keep  his  bal 
ance.     This  seems  to  be  the  reason  why  children  learn  to 

Where  is  the  centre  of  a  man's  gravity  1  Why  will  a  man  fall  with 
a  slight  inclination,  when  his  feet  and  arms  are  tied  1  Why  cannot  one 
who  stands  with  his  heels  against  a  wall  stoop  forward  1  Why  does  a 
person  walk  most  firmly,  who  turns  his  toes  outward  1  Why  does  not 
a  child  walk  as  soon  as  he  can  stand  1 


CENTRE  OF  INERTIA.  t>l 

waik  with  so  much  difficulty,  for  after  they  have  strength 
to  stand,  it  requires  considerable  experience,  so  to  balance 
the  body,  as  to  set  one  foot  before  the  other  without  falling. 

206.  By  experience  in  the  ark  of  balancing,  or  of  keeping 
the  centre  of  gravity  in  a  line  over  the  base,  men  sometimes 
perform  things,  that,  at  first  sight,  appear  altogether  beyond 
human   power,  such  as  dining  with  the  table  and  chair 
standing  on  a  single  rope,  dancing  on  a  wire,  &c. 

207.  No  form,  under  which  matter  exists,  escapes  the  ge- 
neral law  of  gravity,  and  hence  vegetables,  as  well  as  ani- 
mals, are  formed  with  reference  to  the  position  of  this  centre, 
in  respect  to  the  base. 

It  is  interesting,  in  reference  to  this  circumstance,  to  ob- 
serve how  exactly  the  tall  trees  of  the  forest  conform  to  this 
law. 

208.  The  pine,  which  grows  a  hundred  feet  high,  shoots 
up  with  as  much  exactness,  with  respect  to  keeping  its  cen- 
tre of  gravity  within  the  base,  as  though  it  had  been  direct- 
ed by  the  plumb  line  of  a  master  builder.  Its  limbs  towards 
the  top  are  sent  off  in  conformity  to  the  same  law  ;  each  one 
growing  in  respect  to  the  other,  so  as  to  preserve  a  due 
balance  between  the  whole. 

209.  It  may  be  observed,  also,  that  where  many  trees 
grow  near  each  other,  as  in  thick  forests,  and  consequently 
where  the  wind  can  have  but  little  effect  on  each,  that  they 
always  grow  taller  than  when  standing  alone  on  the  plain. 
The  roots  of  such  trees  are  also  smaller,  and  do  not  strike 
so  deep  as  those  of  trees  standing  alone.     A  tall  pine,  in  the 
midst  of  the  forest,  would  be  thrown  to  the  ground  by  the 
first  blast  of  wind,  were  all  those  around  it  cut  away. 

Thus,  the  trees  of  the  forest,  not  only  grow  so  as  to  pre- 
serve their  centres  of  gravity,  but  actually  conform,  in  a  cer- 
tain senste,  to  their  situation. 

CENTRE  OF  INERTIA. 

210.  It  will  be  remembered  that  inertia,  (21)  is  one  of 
the  inherent,  or  essential  properties  of  matter,  and  that  it  is 
in  consequence  of  this  property,  when  bodies  are  at  rest,  that 
they  never  move  without  the  application  of  force,  and  when 

In  what  does  the  art  of  balancing,  or  walking  on  a  rope,  consist  ? 
What  is  observed  in  the  growth  of  the  trees  of  the  forest,  in  respect  to 
the  laws  of  gravity  1  What  effect  does  inertia  have  on  bodies  at  rest  7 
What  effect  does  it  have  on  bodies  in  motion  1 


62  EQUILIBRIUM 

once  in  motion,  that  they  never  cease  moving  without  some 
external  cause. 

211.  Now,  inertia,  though,  like  gravity,  it  resides  equally 
in  every  particle  of  matter,  must  have,  like  gravity,  a  centre 
in  each  particular  body,  and  this  centre  is  the  same  with 
that  of  gravity. 

212.  In  a  bar  of  iron,  six  feet  long  and  two  inches  square, 
the  centre  of  gravity  is  just  three  feet  from  each  end,  or  ex- 
actly in  the  middle.     If,  therefore,  the  bar  is  supported  at 
this  point,  it  will  balance  equally,  and  because  there  are 
equal  weights  on  both  ends,  it  will  not  fall.     This,  there- 
fore, is  the  centre  of  gravity. 

Now  suppose  the  bar  should  be  raised  by  raising  up  the 
centre  of  gravity,  then  the  inertia  of  all  its  parts  would  be 
overcome  equally  with  that  of  the  middle.  The  centre  of 
gravity  is,  therefore,  the  centre  of  inertia. 

213.  The  centre  of  inertia,  being  that  point  which,  being 
lifted,  the  whole  body  is  raised,  is  not,  therefore,  always  at 
the  centre  of  the  body. 

214.  Thus,  suppose  the  same  bar               Fig.  29. 
of  iron,  whose  inertia   was   over- 
come by  raising  the  centre,  to  have  s~^\ 

balls  of  different  weights  attached  \^J 

to  its  ends ;  then  the  centre  of  iner- 
tia would  no  longer  remain  in  the  middle  of  the  bar,  but 
would  be  changed  to  the  point  a,  fig.  29,  so  that  to  lift  the 
whole,  this  point  must  be  raised,  instead  of  the  middle,  as 
before. 

EQUILIBRIUM. 

215.  When  two  forces  counteract,  or  balance  each  other, 
they  are  said  to  be  in  equilibrium. 

216.  It  is  not  necessary  for  this  purpose,  that  the  weights 
opposed  to  each  other  should  be  equally  heavy,  for  we  have 
just  seen  that  a  small  weight,  placed  at  a  distance  from 
the  centre  of  inertia,  will  balance  a  large  one  placed  near 
it.     To  produce  equilibrium,  it  is  only  necessary,  that  the 
weights  on  each  side  of  the  support  should  mutually  coun- 
teract each  other,  or  if  set  in  motion,  that  their  momenta 
should  be  equal. 

Is  the  centre  of  inertia,  and  that  of  gravity,  the  same  1  Where  is  the 
centre  of  inertia  in  a  body,  or  a  system  of  bodies  1  Why  is  the  point 
of  inertia  changed,  by  fixing  different  weights  to  the  ends  of  the  iron 
oar*?  What  is  meant  by  equilibrium  1  To  produce  equilibrium,  must 
the  weights  be  equal  ? 


CURVILINEAR  MOTION.  53 

A  pair  of  scales  are  in  equilibrium,  when  the  beam  is  m 
a  horizontal  position. 

217.  To  produce  equilibrium  in  solid  bodies,  therefore,  it 
is  only  necessary  to  support  the  centre  of  inertia,  or  gravity. 

218.  If  a  body,  or  several  bod-  Fig.  30. 
ies,  connected,  be  suspended  by  a 

string,  as  in  fig.  30,  the  point  of 
support  is  always  in  a  perpendic- 
ular line  above  the  centre  of  in- 
ertia. The  plumb  line  d,  cuts  the 
bar  connecting-  the  two  balls  at 
this  point.  Were  the  two  weights 
in  this  figure  equal,  it  is  evident 
that  the  hook,  or  point  of  support, 

must  be  in  the  middle  of  the  string,  to  preserve  the  hori- 
zontal position. 

219.  When  a  man  stands  on  his  right  foot,  he  keeps  him- 
self in  equilibrium,  by  leaning  to  the  right,  so  as  to  bring 
his  centre  of  gravity  in  a  perpendicular  line  over  the  foot 
on  which  he  stands. 

CURVILINEAR,  OR  BENT  MOTION. 

220.  We  have  seen  that  a  single  force  acting  on  a  body, 
(153,)  drives  it  straight  forward,  and  that  two  forces  acting1 
crosswise,  drive  it  midway  between  the  two,  or  give  it  a  di- 
agonal direction,  (160.) 

221.  Curvilinear  motion  differs  from  both  these,  the  di- 
rection of  the  body  being  neither  straight  forward,  nor  di- 
agonal, but  through  a  line  which  is  curved. 

222.  This  kind  of  motion  may  be  in  any  direction,  but 
when  it  is  produced  in  part  by  gravity,  its  direction  is  al- 
ways towards  the  earth. 

223.  A  stream  of  water  from  an  aperture  in  the  side  of  a 
vessel,  as  it  falls  towards  the  ground,  is  an  example  of  a 
curved  line ;  and  a  body  passing  through  such  a  line,  is  said 
to  have  curvilinear  motion.     Any  body  projected  forward, 
as  a  cannon  ball  or  rocket,  falls  to  the  earth  in  a  curved  line. 

224.  It  is  the  action  of  gravity  across  the  course  of  the 
stream,  or  the  path  of  the  ball,  that  bends  it  downwards,  and 


When  is  a  pair  of  scales  in  equilibrium  1  When  a  body  is  suspended 
by  a  string,  where  must  the  support  be  with  respect  to  the  point  of  in- 
ertia 1  What  is  meant  by  curvilinear  motion  1  What  are  examples  of 
this  kind  of  motion  1  What  two  forces  produce  this  motion  ? 

5* 


54  CURVILINEAR  MOTION. 

makes  it  form  a  curve.     The  motion  is  therefore  the  result 
of  two  forces,  that  of  projection,  and  that  of  gravity. 

225.  The  shape  of  the  curve  will  depend  on  the  velocity 
of  the  stream  or  ball.     When  the  pressure  of  the  water  is 
great,  the  stream,  near  the  vessel,  is  nearly  horizontal,  be- 
cause its  velocity  is  in  proportion  to  the  pressure.     When 
a  ball  first  leaves  the  cannon,  it  describes  but  a  slight  curve, 
because  its  projectile  velocity  is  then  greatest. 

The  curves  described  by  jets  of  water,  under  different 
degrees  of  pressure,  are  readily  illustrated  by  tapping  a  tall 
vessel  in  several  places,  one  above  the  other. 

226.  Suppose   fig.    31    be  Fig.  31. 
such  a  vessel,  filled  with  wa- 
ter, and  pierced  as  represent- 
ed.    The  streams   will   form 

curves  differing  from  each 
other,  as  seen  in  the  figure, 
Where  the  projectile  force  is 
greatest,  as  from  the  lower 
orifice,  the  stream  reaches  the 
ground  at  the  greatest  distance 
from  the  vessel,  this  distance 
decreasing,  as  the  pressure 
becomes  less  towards  the  top 
of  the  vessel.  The  action  of 
gravity  being  always  the  same,^ 
the  shape  of  the  curve  described, .as  just  stated,  must  depend 
on  the  velocity  of  the  moving  body;  but  whether  the  pro- 
jectile force  be  great  or  small,  the  moving  body,  if  thrown 
horizontally,  will  reach  the  ground  from  the  same  height 
in  the  same  time. 

227.  This,  at  first  thought,  would  seem  improbable,  for, 
without  consideration,  most  persons  would  assert,  very  posi- 
tively, that  if  two  cannon  were  fired  from  the  same  spot,  at  the 
same  instant,  and  in  the  same  direction,  one  of  the  balls  fall- 
ing half  a  mile,  and  the  other  a  mile  distant,  that  the  ball 
which  went  to  the  greatest  distance,  would  take  the  most 
time  in  performing  its  journey. 

228.  But  it  must  be  remembered,  that  the  projectile  force 

On  what  does  the  shape  of  the  curve  depend  1  How  are  the  curves 
described  by  jets  of  water  illustrated  1  What  difference  is  there  in  re- 
spect to  the  time  taken  by  a  body  to  reach  the  ground,  whether  the  curve 
be  great  or  small  1  Why  do  bodies  forming  different  curves  from  the 
same  height,  reach  the  ground  at  the  same  time  1 


CURVILINEAR  MOTION. 


55 


does  not  in  the  least  interfere  with  the  force  of  gravity.  A 
ball  flying  horizontally  at  the  rate  of  a  thousand  feet  per 
second,  is  attracted  downwards  with  precisely  the  same  force 
as  one  flying  only  a  hundred  feet  per  second,  and  must 
therefore  descend  the  same  distance  in  the  same  time. 

229.  The  distance  to  which  a  ball  will  go,  depends  on  the 
force  of  impulse  given  it  the  first  instant,  and  consequently 
on  its  projectile  velocity.     If  it  moves  slowly,  the  distance 
will  be  short— if  more  rapidly,  the  space  passed  over  will 
be  greater.     It  makes  no  difference,  then,  in  respect  to  the 
descent  of  the  ball,  whether  its  projectile  motion  be  fast,  or 
slow,  or  whether  it  moves  forward  at  all. 

230.  This  is  demonstrated  by  experiment.     Suppose  a 
cannon  to  be  loaded  with  a  ball,  and  placed  on  the  top  of  a 
tower,  at  such  a  height  from  the  ground,  that  it  would  take 
just  three  seconds  for  a  cannon  ball  to  descend  from  it  to  the 
ground,  if  let  fall  perpendicularly.     Now  suppose  the  can- 
non to  be  fired  in  an  exact  horizontal  direction,  and  at  the 
same  instant,  the  ball  to  be  dropped  towards  the  ground. 
They  will  both  reach  the  ground  at  the  same  instant,  pro- 
vided its  surface  be  a  horizontal  plane  from  the  foot  of  the 
tower  to  the  place  where  the  projected  ball  strikes. 

281.  This  will  be  made  plain  by  fig.  32,  where  a  is  the 
perpendicular  line  of  the  descending  ball,  c  b  the  curvilinear 
path  of  that  projected  from  the  cannon,  and  d,  the  horizon- 
tal line  from  the  foot  of  the  tower. 
Fig.  32. 


Suppose  two  balls,  one  flying  at  the  rate  of  a  thousand,  and  the  other 
at  the  rate  of  a  hundred  feet  per  second,  which  would  descend  most 
during  the  second  1  Does  it  make  any  difference  in  respect  to  the  de- 
scent of  the  ball,  whether  it  has  a  projectile  motion  or  not  1  Suppose, 
then,  one  ball  be  fired  from  a  cannon,  and  another  let  fall  from  the  same 
height  at  the  same  instant,  would  they  both  reach  the  ground  at  the 
same  time  1  Explain  fig.  32,  showing  the  reason  why  the  two  balls  will 
reach  the  ground  at  the  same  time. 


66  CURVILINEAR  MOTION. 

The  reason  why  the  two  balls  reach  the  ground  at  the 
same  time,  is  easily  comprehended. 

232.  During  the  first  second,  suppose  that  the  ball  which 
is  dropped,  reaches  1 ;  during  the  next  second  it  falls  to  2; 
and  at  the  end  of  the  third  second,  it  strikes  the  ground. 
Meantime,  the  ball  shot  from  the  cannon  is  projected  for- 
ward with  such  velocity  as  to  reach  4  in  the  same  time  thai 
the  other  is  falling  to  1.     But  the  projected  ball  falls  down- 
ward exactly  as  fast  as  the  other,  for  it  meets  the  line  1,  4, 
which  is  parallel  to  the  horizon,  at  the  same  instant.   During 
the  next  second,  the  projected  ball  reaches  5,  while  the  other 
arrives  at  two  5  and  here  again  they  have  both  descended 
through  the  same  downward  space,  as  is  seen  by  the  line  2, 
5,  which  is  parallel  with  the  other.     During  the  third  sec- 
ond, the  ball  from  the  cannon  will  have  nearly  spent  its  pro- 
jectile force,  and,  therefore,  its  motion  downward  will  be 
greater,  while  its  motion  forward  will  be  less  than  before. 
The  reason  of  this  will  be  obvious,  when  it  is  considered, 
that  in  respect  to  gravity,  both   balls   follow  exactly  the 
same  law,  and  fall  through  equal  spaces  in  equal  times. 
Therefore,  as.  the  falling  ball  descends  through  the  greatest 
space  during  the  last  second,  so  that  from  the  cannon,  having 
now  a  less  projectile  motion,  its  downward  motion  is  more 
direct,  and,  like  all  falling  bodies,  its  velocity  is  increased  as 
it  approaches  the  earth. 

233.  From  these  principles  it  may  be  inferred,  that  the 
horizontal  motion  of  a  body  through  the  air,  does  not  in  the 
least  interfere  with  its  gravitating  motion  towards  the  earth, 
and,  therefore,  that  a  rifle  ball,  or  any  other  body  projected 
forward  horizontally,  will  reach  the  ground  in  exactly  the 
same  period  of  time,  as  one  that  is  let  fall  perpendicularly 
from  the  same  height. 

234.  The  two  forces  acting  on  bodies  which  fall  through 
curved  lines,  are  the  same  as  the  centrifugal  and  centripetal 
forces,  already  explained  ;  the  centrifugal,  in  case  of  the  ball, 
being  caused  by  the  powder — the  centripetal,  being  the  ac 
tion  of  gravity. 

235.  Now,  it  is  obvious,  that  the  space  through  which  a 
cannon  ball,  or  any  other  body,  can  be  thrown,  depends  on 

Why  does  the  ball  approach  the  earth  more  rapidly  in  the  last  part 
of  the  curve,  than  in  the  first  part  ?  What  is  the  force  called  which 
throws  a  ball  forward  ?  What  is  that  called,  which  brings  it  to  the 
ground  1  On  what  does  the  distance  to  which  a  projected  body  may  be 
thrown  depend  1  Why  does  the  distance  depend  on  the  velocity  1 


CURVILINEAR  MOTION.  57 

the  velocity  with  which  it  is  projected,  for  the  attraction  of 
gravitation,  and  the  resistance  of  the  air,  acting  perpetually, 
the  time  which  a  projectile  can  be  kept  in  motion,  through 
the  air,  is  only  a  few  moments. 

236.  If,  however,  the  projectile  be  thrown  from  an  ele- 
vated situation,  it  is  plain,  that  it  would  strike  at  a  greater 
distance  than  if  thrown  on  a  level,  because  it  would  remain 
longer  in  the  air.     Every  one  knows  that  he  can  throw  a 
stone  to  a  greater  distance,  when  standing  on  a  steep  hill, 
than  when  standing  on  the  plain  below. 

237.  Bonaparte,  it  is  said,  by  elevating  the  range  of  his 
shot,  bombarded  Cadiz  from  the  distance  of  five  miles.    Per- 
haps, then,  from  a  high  mountain,  a  cannon  ball  might  be 
thrown  to  the  distance  of  six  or  seven  miles. 

238.  Suppose  the  cir-  Fi^  33. 
cle,   fig.  33,  to   be   the 

earth,  and  a,  a  high 
mountain  on  its  surface. 
Suppose  that  this  moun- 
tain reaches  above  the 
atmosphere,  or  is  fifty 
miles  high,  then  a  can- 
non ball  might  perhaps 
reach  from  a  to  b,  a  dis- 
tance of  eighty  or  a 
hundred  miles,  because 
the  resistance  of  the  at- 
mosphere being  out  of 
the  calculation,  it  would 
have  nothing  to  contend  with,  except  the  attraction  of  gravi- 
tation. If,  then,  one  degree  of  force,  or  velocity,  would 
send  it  to  b,  another  would  send  it  to  c :  and  if  the  force  was 
increased  three  times,  it  would  fall  at  d,  and  if  four  times, 
it  would  pass  to  e.  If  now  we  suppose  the  force  to  be  about 
ten  times  greater  than  that  with  which  a  cannon  ball  is  pro- 
jected, it  would  not  fall  to  the  earth  at  any  of  these  points, 
but  would  continue  its  motion,  until  it  again  came  to  the 
point  &,  the  place  from  which  it  was  first  projected.  It 
would  now  be  in  equilibrium,  the  centrifugal  force  being 
just  equal  to  that  of  gravity,  and  therefore  it  would  perform 


Explain  fig.  33.  Suppose  the  velocity  of  a  cannon  ball  shot  from  a 
a  mountain  50  miles  high,  to  be  ten  times  its  usual  rate,  where  would 
it  stop  1  When  vould  this  ball  be  in  equilibrium  1 


58  RESULTANT  MOTION. 

another,  and  another  revolution,  and  so  continue  to  revolve 
around  the  earth  perpetually. 

239.  The  reason  why  the  force  of  gravity  will  not  ulti- 
mately bring  it  to  the  earth,  is,  that  during  the  first  revolu- 
tion, the  effect  of  this  force  is  just  equal  to  that  exerted  in 
any  other  revolution,  but  neither  more  nor  less;  and,  there- 
fore, if  the  centrifugal  force  was  sufficient  to  overcome  this 
attraction  during  one  revolution,  it  would  also  overcome  it 
during  the  next.     It  is  supposed,  also,  that  nothing  tends  to 
affect  the  projectile  force  except  that  of  gravity,  and  the 
force  of  this  attraction  would  be  no  greater  during  any  other 
revolution,  than  during  the  first. 

240.  In  other  words,  the  centrifugal  and  centripetal  forces 
are  supposed  to  be  exactly  equal,  and  to   mutually  balance 
each  other ;  in  which  case,  the  ball  would  be,  as  it  were, 
suspended  between  them.     As  long,  therefore,  as  these  two 
forces  continued  to  act  with  the  same  power,  the  ball  would 
no  more  deviate  from  its  path,  than  a  pair  of  scales  would 
lose  their  balance  without  more  weight  on  one  side  than  on 
the  other. 

241.  It  is  these  two  forces  which  retain  the  heavenly 
bodies  in  their  orbits,  and  in  the  case  we  have  supposed,  our 
cannon  ball  would  become  a  little  satellite,  moving  perpetu- 
ally round  the  earth. 

RESULTANT  MOTION. 

242.  Suppose  two  men  to  be  sailing  in  two  boats,  each  at 
the  rate  of  four  miles  an  hour,  at  a  short  distance  opposite 
to  each  other,  and  suppose  as  they  are  sailing  along  in  this 
manner,  one  of  the  men  throws  the  other  an  apple.     In  re- 
spect to  the  boats,  the  apple  would  pass  directly  across,  from 
one  to  the  other,  that  is,  its  line  of  direction  would  be  per- 
pendicular to  the  sides  of  the  boats.     But  its  actual  line 
through  the  air  would  be  oblique,  or  diagonal,  in  respect  to 
the  sides  of  the  boats,  because  in  passing  from  boat  to  boat, 
it  is  impelled  by  two  forces,  viz.,  the  force  of  the  motion  of 
the  boat  forward,  and  the  force  by  which  it  is  thrown  by  the 
hand  across  this  motion. 

Why  would  not  the  force  of  gravity  ultimately  bring  the  ball  to  the 
earth  1  After  the  first  revolution,  if  the  two  forces  continued  the  same, 
would  not  the  motion  of  the  ball  be  perpetual?  Suppose  two  boats,  sail- 
ing at  the  same  rate,  and  in  the  same  direction,  if  an  apple  be  tossed 
from  one  to  the  other,  what  will  be  its  direction  in  respect  to  the  boats  ? 
What  would  be  its  line  through  the  air,  in  respect  to  the  boats  1 


RESULTANT  MOTION.  59 

243.  This  diagonal  motion  of  the  apple  is  called  the  re- 
sultant, or  the  resulting  motion,  because  it  is  the  effect,  or 
result,  of  two  motions,  resolved  into  one.     Perhaps  this  will 
be  more  clear  by  fig.  34,  where  Fig.  34. 

a  b,  and  c  d,  are  supposed  to  be 

the  sides  of  the  two  boats,  and  & 

the  line  e,  f,  that  of  the  apple. 
Now  the  apple  when  thrown, 
has  a  motion  with  the  boat  at  the 

rate  of  four  miles  an  hour,  from  c 

c  towards  d,  and  this  motion  is  e 

supposed  to  continue  just  as  though  it  had  remained  in  the 
boat.  Had  it  remained  in  the  boat  during  the  time  it  was 
passing  from  e  to  f,  it  would  have  passed  from  e  to  h.  But 
we  suppose  it  to  have  been  thrown  at  the  rate  of  eight  miles 
an  hour  in  the  direction  towards  g,  and  if  the  boats  are 
moving  south,  and  the  apple  thrown  towards  the  east,  it 
would  pass  in  the  same  time,  twice  as  far  towards  the  east 
as  it  did  towards  the  south.  Therefore,  in  respect  to  the 
boats,  the  apple  would  pass  in  a  perpendicular  line  from  the 
side  of  one  to  that  of  the  other,  because  they  are  both  in 
motion;  but  in  respect  to  one  perpendicular  line,  drawn  from 
the  point  where  the  apple  was  thrown,  and  a  parallel  line 
with  this,  drawn  from  the  point  where  it  strikes  the  other 
boat,  the  line  of  the  apple  would  be  oblique.  This  will  be 
clear,  when  we  consider,  that  when  the  apple  is  thrown,  the 
boats  are  at  the  points  e  and  g,  and  that  when  it  strikes,  they 
are  at  h  and  /  these  two  points  being  opposite  to  each  other. 
The  line  e  f,  through  which  the  apple  is  thrown,  is  called 
the  diagonal  of  a  parallelogram,  as  already  explained  under 
compound  motion. 

244.  On  the  above  principle,  if  two  ships,  during  a  bat- 
tle, are  sailing  before  the  wind  at  equal  rates,  the  aim  of  the 
gunners  will  be  exactly  the  same  as  though  they  stood  still; 
whereas,  if  the  gunner  fires  from  a  ship  standing  still,  at 
another  under  sail,  he  takes  his  aim  forward  of  the  mark 
he  intends  to  hit,  because  the  ship  would  pass  a  little  for- 
ward while  the  ball  is  going  to  her.     And  so,  on  the  con- 

What  is  this  kind  of  motion  called  1  Why  is  it  called  resultant  mo- 
tion'? Explain  fig.  34.  Why  would  the  line  of  the  apple  be  actually 
perpendicular  in  respect  to  the  boats,  but  oblique  in  respect  to  parallel 
lines  drawn  from  where  it  was  thrown,  and  where  it  struck  1  How  is 
this  further  illustrated  1  When  the  ships  are  in  equal  motion,  where 
does  the  gunner  take  his  aim'?  Why  does  he  aim  forward  of  the  mark; 
when  the  other  ship  is  in  motion  1 


60  PENDULUM, 

trary,  if  a  ship  in  motion  fires  at  another  standing  still,  the 
aim  must  be  behind  the  mark,  because,  as  the  motion  of  the 
ball  partakes  of  that  of  the  ship,  it  will  strike  forward  of 
the  point  aimed  at. 

245.  For  the  same  reason,  if  a  ball  be  dropped  from  the 
topmast  of  a  ship  under  sail,  it  partakes  of  the  motion  of  the 
ship  forward,  and  will  fall  in  a  line  with  the  mast,  and  strike 
the  same  point  on  the  deck,  as  though  the  ship  stood  still. 

246.  If  a  man  upon  the  full  run  drops  a  bullet  before  him 
from  the  height  of  his  head,  he  cannot  run  so  fast  as  to  over- 
take it  before  it  reaches  the  ground. 

247.  It  is  on  this  principle,  that  if  a  cannon  ball  be  shot 
up  vertically  from  the  earth,  it  will  fall  back  to  the  same 
point ;  for  although  the  earth  moves  forward  while  the  ball 
is  in  the  air,  yet  as  it  carries  this  motion  with  it,  so  the  ball 
moves  forward  also,  in  an  equal  degree,  and  therefore  comes 
down  at  the  same  place. 

248.  Ignorance  of  these  laws  induced  the  story-making 
sailor  to  tell  his  comrades,  that  he  once  sailed  in  a  ship 
which  went  so  fast,  that  when  a  man  fell  from  the  mast- 
head, the  ship  sailed  away  and  left  the  poor  fellow  to  strike 
into  the  water  behind  her. 

PENDULUM. 

249.  A  pendulum  is  a  heavy  body,  such  as  a  piece  of 
brass,  or  lead,  suspended  by  a  wire  or  cord,  so  as  to  swing 
backwards  and  forwards. 

When  a  pendulum  swings,  it  is  said  to  vibrate  ;  and  that 
J  .        part  of  a  circle  through  which  it  vibrates,  is  called  its  arc. 

250.  The  times  of  the  vibration  of  a  pendulum  are  very 
nearly  equal,  whether  it  pass  through  a  greater  or  less  part 
of  its  arc. 

Suppose  a  and  b,  fig.  35,  to  be  two  pendulums  of  equal 
length,  and  suppose  the  weights  of  each  are  carried,  the  one 
to  c,  and  the  other  to  dt  and  both  let  fall  at  the  same  in- 

If  a  ship  in  motion  fires  at  one  standing  still,  where  must  be  the  aiml 
Why,  in  this  case,  must  the  aim  be  behind  the  mark  1  What  other  il- 
lustrations are  given  of  resultant  motion 7  What  is  a  pendulum? 
What  is  meant  by  the  vibration  of  a  pendulum  ?  What  is  that  part  of  a 
circle  called,  through  which  it  swings  1  Why  does  a  pendulum  vibrate 
in  equal  time,  whether  it  goes  through  a  small  or  large  part  of  its  arc  1 


PEND  JLUM. 


mstant ;  their  vi-  Pig.  35. 

brations  would 
be  equal  in  re- 
spect to  time, 
the  one  pass- 
ing through  its 
arc  from  c  to  e, 
and  so  back 
again,  in  the 
same  time  that 
.he  other  passes 
from  dtof,  and  back  again. 

251.  The  reason  of  this  appears  to  be,  that  when  the  pen- 
dulum is  raised  high,  the  action  of  gravity  draws  it  more 
directly  downwards,  and  it  therefore  acquires,  in  falling,  a 
greater  comparative  velocity  than  is  proportioned  to   the 
trifling  difference  of  height. 

252.  In  the  common  clock,  the  pendulum  is  connected 
with  wheel  work,  to  regulate  the  motion  of  the  hands,  and 
with  weights,  by  which  the  whole  is  moved.     The  vibra- 
tions of  the  pendulum  are  numbered  by  a  wheel  having  sixty 
teeth,  which  revolves  once  in  a  minute.     Each  tooth,  there- 
fore, answers  to  one  swing  of  the  pendulum,  and  the  wheel 
moves  forward  one  tooth  in  a  second.    Thus  the  second  hand 
revolves  once  in  every  sixty  beats  of  the  pendulum,  and  as 
these  beats  are  seconds,  it  goes  round  once  in  a  minute.    By 
the  pendulum,  the  whole  machine  is  regulated,  for  the  clock 
goes  faster,  or  slower,  according  to  its  number  of  vibrations 
in  a  given  time.     The  number  of  vibrations  which  a  pendu- 
lum  makes  in  a  given  time,  depends  upon  its  length,  because 
a  long  pendulum  does  not  perform  its  journey  to  and  from 
the  corresponding  points  of  its  arc  so  soon  as  a  short  one. 

253.  As  the  motion  of  the  clock  is  regulated  entirely  by 
the  pendulum,  and  as  the  number  of  vibrations  are  as  its 
length,  the  least  variation  in  this  respect  will  alter  its  rate 
of  going.     To  beat  seconds,  its  length  must  be  about  39 
inches.     In  the  common  clock,  the  length  is  regulated  by  a 
screw,  which  raises  and  lowers  the  weight.    But  as  the  rod 
to  which  the  weight  is  attached,  is  subject  to  variations  of 

Describe  the  common  clock.  How  many  vibrations  has  the  pendu- 
lum in  a  minute  1  On  what  depends  the  number  of  vibrations  which 
a  pendulum  makes  in  a  given  time  1  What  is  the  medium  length  of  a 
pendulum  beating  seconds  ?  Why  does  a  common  clock  go  faster  in 
winter  than  in  summer"? 


62 


PENDULUM. 


length  in  consequence  of  the  change  of  the  seasons,  being 
contracted  by  cold  and  lengthened  by  heat,  the  common 
clock  goes  faster  in  winter  tha^  in  summer. 

254.  Various  means  have  been  contrived  to  counteract 
the  effects  of  these  changes,  so  that  the  pendulums  may  con- 
tinue the  same  length  the  whole  year.     Among  inventions 
for  this  purpose,  the  gridiron  pendulum  is  considered  the 
best.     It  is  so  called,  because  it  consists  of  several  rods  of 
metal  connected  together  at  each  end. 

255.  The  principle  on  which  this  pendulum  is  construct- 
ed, is  derived  from  the  fact,  that  some  metals  dilate  more  by 
the  same  degrees  of  heat  than  others.     Thus,  brass  will  di- 
late twice  as  much  by  heat,  and  consequently  contract  twice 
as  much  by  cold,  as  steel.     If  then  these  differences  could 
be  made  to  counteract  each  other  mutually,  given  points  at 
each  end  of  a  system  of  such  rods  would  remain  stationary 
the  year  round,  and  thus  the  clock  would  go  at  the  same 
rate  in  all  climates,  and  during  all  seasons. 

This  important  object  is  accomplished  by  the   Fig.  36. 
following  means. 

256.  Suppose  the   middle  rod,  fig.  36,    to  be        l^ 
made  of  brass,  and  the  two  outside  ones  of  steel, 

all  of  the  same  length.  Let  the  brass  rod  be  firmly 
fixed  to  the  cross  pieces  at  each  end.  Let  the  steel 
rod  a,  be  fixed  to  the  lower  cross  piece,  and  Z>,  to 
the  upper  cross  piece.  The  rod  a,  at  its  upper  end, 
passes  through  the  cross  piece,  and,  in  like  man- 
ner, b  passes  through  the  lower  one.  This  is 
done  to  prevent  these  small  rods  from  playing 
backwards  and  forwards  as  the  pendulum  swings. 

257.  Now,  as  the  middle  rod  is  lengthened  by 
the  heat  twice  as  much  as  the  outside  ones,  and 
the  outside  rods  together  are  twice  as  long  as  the 
middle  one,  the  actual  length  of  the  pendulum  can 
neither  be  increased  nor  diminished  by  the  variations  of 
temperature. 


What  is  necessary  in  respect  to  the  pendulum,  to  make  the  clock  go 
true  the  year  round  1  What  is  the  principle  on  which  the  gridiron  pen- 
dulum is  constructed  1  What  are  the  metals  of  which  this  instrument 
is  made  1  Explain  fig.  36,  and  give  the  reason  why  the  length  of  the 
pendulum  will  not  change  by  the  variations  of  temperature  1 


PENDULUM.  63 

258.  To  make  this  still  plainer,  sunpose  the     Fig.  37. 
lower  cross  piece,  fig.  37,  to  be  standing  on  a  ta- 

ble,  so  that  it  could  not  be  lengthened  downwards, 
and  suppose,  by  the  heat  of  summer,  the  middle 
rod  of  brass  should  increase  one  inch  in  length. 
This  would  elevate  the  upper  cross  piece  an  inch, 
but  at  the  same  time  the  steel  rod  a,  swells  half 
an  inch,  and  the  steel  rod  b,  half  an  inch,  there- 
fore, the  iwo  points,  c  and  d,  would  remain  exact- 
ly at  the  same  distance  from  each  other. 

259.  As  it  is  the  force  of  gravity  which  draws  the  weight 
of  the  pendulum  from  the  highest  point  of  its  arc  down- 
wards, and  as  this  force  increases,  or  diminishes,  as  bodies 
approach  towards  the  centre  of  the  earth,  or  recede  from  it, 
so  the  pendulum  will  vibrate  faster,  or  slower,  in  proportion 
as  this  attraction  is  stronger  or  weaker. 

260.  Now,  it  is  found  that  the  earth  at  the  equator  rises 
higher  from  its  centre  than  it  does  at  the  poles,  for  towards 
the  poles  it  is  flattened.     The  pendulum,  therefore,  being 
more  strongly  attracted  at  the  poles  than  at  the  equator,  vi- 
brates faster.     For  this  reason,  a  clock  that  would  keep 
exact  time  at  the  equator,  would  gain  time  at  the  poles,  for 
the  rate  at  which  a  clock  goes,  depends  on  the  number  of 
vibrations  its  pendulum  makes.     Therefore,  pendulums,  in 
order  to  beat  seconds,  must  be  shorter  at  the  equator,  and 
longer  at  the  poles. 

For  the  same  reason,  a  clock  which  keeps  exact  time  at 
the  foot  of  a  high  mountain,  would  move  slower  on  its  top. 

26 1 .  Metronome. — There  is  a  short  pendulum,  used  by  mu- 
sicians for  marking  time,  which  may  be  made  to  vibrate  fast 
or  slow,  as  occasion  requires.    This  little  instrument  is  call- 
ed a  metronome,  and  besides  the  pendulum,  consists  of  seve- 
ral wheels,  and  a  spiral  spring,  by  which  the  whole  is 
moved.     This  pendulum  is  only  ten  or  twelve  inches  long, 
and  instead  of  being  suspended  by  the  end,  like  other  pendu- 
lums, the  rod   is  prolonged  above  the  point  of  suspension, 
and  there  is  a  ball  placed  near  the  upper,  as  well  as  at  the 
lower  extremity. 

Explain  fig.  37.  What  is  the  downward  force  which  makes  the  pen- 
dulum vibrate  1  Explain  the  reason  why  the  same  clock  would  go  faster 
at  the  poles,  and  slower  at  the  equator.  How  can  a  clock  which  goes 
true  at  the  equator  be  made  to  go  true  at  the  poles  1  Will  a  clock  keep 
equal  time  at  the  foot,  and  on  the  top  of  a  high  mountain  1  Why  will 
it  not  1  What  is  the  metronome  1  How  does  this  pendulum  differ  from 
common  pendulums? 


64 


MECHANICS. 


262.  This  arrangement  will  be  Fig.  38. 
Tiederstood  by  fig.  38,  where  a  is  the 

axis  of  suspension,  b  the  upper  ball, 
and  c  the  lower  one.  Now  when 
this  pendulum  vibrates  from  the 
point  a,  the  upper  ball  constantly 
retards  the  motion  of  the  lower  one, 
by  in  part  counterbalancing  its 
weight,  and  thus  preventing  its  full 
velocity  downwards. 

263.  Perhaps  this  will  be  more 
apparent,  by  placing  the  pendulum, 
fig.  39,  for  a  moment  on  its  side,  and 

across  a  bar,  at  the  point  of  suspen-  Fig.  39. 

sion.  In  this  position,  it  will 
be  seen,  that  the  little  ball 
would  prevent  the  large  one  — Q- 
from  falling  with  its  full  weight, 
since,  were  it  moved  to  a  cer- 
tain distance  from  the  point  of  suspension,  it  would  balance 
the  large  one,  so  that  it  would  not  descend  at  all.  It  is 
plain,  therefore,  that  the  comparative  velocity  of  the  large 
ball,  will  be  in  proportion  as  the  small  one  is  moved  to  a 
greater  or  less  distance  from  the  point  of  suspension.  The 
metronome  is  so  constructed,  the  little  ball  being  made  to 
move  up  and  down  on  the  rod,  at  pleasure,  and  thus  its  vi- 
brations are  made  to  beat  the  time  of  a  quick,  or  slow  tune 
as  occasion  requires. 

By  this  arrangement,  the  instrument  is  made  to  vibrate 
every  two  seconds,  or  every  half,  or  quarter  of  a  second,  at 
pleasure. 


o 


MECHANICS. 

264.  Mechanics  is  a  science  which  investigates  the  laws 
and  effects  of  force  and  motion. 

265.  The  practical  object  of  this  science  is,  to  teach  the 
best  modes  of  overcoming  resistances  by  means  of  mechan- 
ical powers,  and  to  apply  motion  to  useful  purposes,  by 
means  of  machinery. 


How  does  the  upper  ball  retard  the  motion  of  the  lower  one  ?  How 
is  the  metronome  made  to  go  faster  or  slower,  at  pleasure  1  What  is 
mechanics'?  What  is  the  object  of  this  science? 


MECHANICS.  65 

266.  A  machine  is  any  instrument  by  which  power,  mo* 
(ion,  or  velocity,  is  applied,  or  regulated. 

267.  A  machine  may  be  very  simple,  or  exceedingly  com- 
plex.    Thus,  a  pin  is  a  machine  for  fastening  clothes,  and  a 
steam  engine  is  a  machine  for  propelling  mills  and  boats. 

268.  As  machines  are  constructed  for  a  vast  variety  of 
purposes,  their  forms,  powers,  and  kinds  of  movement,  must 
depend  on  their  intended  uses. 

269.  Several  considerations  ought  to  precede  the  actual 
construction  of  a  new  or  untried  machine ;  for  if  it  does  not 
answer  the  purpose  intended,  it  is  commonly  a  total  loss  to 
the  builder. 

270.  Many  a  man,  on  attempting  to  apply  an  old  princi- 
ple to  a  new  purpose,  or  to  invent  a  new  machine  for  an  old 
purpose,  has  been  sorely  disappointed,  having  found,  when 
too  late,  that  his  time  and  money  had  been  thrown  away, 
for  want  of  proper  reflection,  or  requisite  knowledge. 

271.  If  a  man,  for  instance,  thinks  of  constructing  a  ma- 
chine for  raising  a  ship,  he  ought  to  take  into  consideration 
the  inertia,  or  weight,  to  be  moved — the/orcgtobe  applied 
— the  strength  of  the  materials,  and  the  space,  or  situation, 
he  has  to  work  in.    For,  if  the  force  applied,  or  the  strength 
of  the  materials,  be  insufficient,  his  machine  is  obviously 
useless;  and  if  the  force  and  strength  be  ample,  but  the 
Space  be  wanting,  the  same  result  must  follow. 

272.  If  he  intends  his  machine  for  twisting  the  fibres  of 
flexible  substances  into  threads,  he  may  find  no  difficulty  in 
respect  to  power,  strength  of  materials,  or  space  to  work  in, 
but  if  the  velocity,  direction,  and  kind  of  motion  he  obtains, 
be  not  applicable  to  the  work  intended,  he  still  loses  his 
labour. 

273.  Thousands   of   machines   have   been   constructed, 
which,  so  far  as  regarded  the  skill  of  the  workmen,  the  in- 
genuity of  the  contriver,  and  the  construction  of  the  indi- 
vidual parts,  were  models  of  art  and  beauty;  and,  so  far  as 
could  be  seen  without  trial,  admirably  adapted  to  the  intend- 
ed purpose.     But  on  putting  them  to  actual  use,  it  has  too 
often  been  found,  that  their  only  imperfection  consisted  in  a 
stubborn  refusal  to  do  any  part  of  the  work  intended. 

274.  Now,  a  thorough  knowledge  of  the  laws  of  motion, 
and  the  principles  of  mechanics,  would,  in  many  instances 

What  is  a  machine?   Mention  one  of  the  most  simple,  and  one  of 
the  most  complex  of  machines. 
6* 


66  LEVER. 

at  least,  have  jTevented  all  this  loss  of  labour  and  money, 
and  spared  him  so  much  vexation  and  chagrin,  by  showing 
the  projector  that  his  machine  would  not  answer  the  intend- 
ed purpose. 

275.  The  importance  of  this  kind  of  knowledge  is  there- 
fore obvious,  and  it  is  hoped  will  become  more  so  as  we 
proceed. 

276.  Definitions.— In    mechanics,  as   well   as  in   other 
sciences,  there  are  words  which  must  be  explained,  either 
because  they  are  common  words  used  in  a  peculiar  sense, 
or  because  they  are  terms  of  art,  not    in   common   use. 
All  technical  terms  will  be  as  much  as  possible  avoided,  but 
still  there  are  a  few,  which  it  is  necessary  here  to  explain. 

277.  Force  is  the  means  by  which  bodies  are  set  in  mo- 
tion, kept  in  motion,  and  when  moving,  are  brought  to  rest. 
The  force  of  gunpowder  sets  the  ball  in  motion,  and  keeps 
it  moving,  until  the  force  of  resisting  air,  and  the  force  of  gra- 
vity, bring  it  to  rest. 

278.  Power  is  the  means  by  which  the  machine  is  moved, 
and  the  force  gained.     Thus  we  have  horse  power,  watei 
power,  and  the  power  of  weights. 

279.  Weight  is  the  resistance,  or  the  thing  to  be  moved 
by  the  force  of  the  power.  Thus,  the  stone  is  the  weight  to  be 
moved  by, the  force  of  the  lever,  or  bar. 

280.  Fulcrum,  or  prop,  is  the  point  or  part  an  which  a 
thing  is  supported,  and  about  which  it  has  more  or  less  mo- 
tion.    In  raising  a  stone,  the  thing  on  which  the  lever  rests, 
is  the  fulcrum. 

281.  In  mechanics,  there  #re   a  few  simple  machines, 
called  the  mechanical  powers,  and  however  mixed,  or  com- 
plex, a  combination  of  machinery  may  be,  it  consists  only  of 
these  few  individual  powers. 

282.  We  shall  not  here  burthen  the  memory  of  the  pu- 
pil with  the  names  of  these  powers,  of  the  nature  of  which 
he  is  at  present  supposed  to  know  nothing,  but  shall  explain 
the  action  and  use  of  each  in  its  turn,  and  then  sum  up  the 
whole  for  his  accommodation. 

THE  LEVER. 

283.  Any  rod,  or  bar,  which  is  used  in  raising  a  weight, 


What  is  meant  by  force  in  mechanics  1  What  is  meant  by  powor  ? 
What  is  understood  by  weight  1  What  is  the  fulcrum  1  Are  the  me- 
chanical powers  numerous,  or  only  few  in  number  ? 


LEVER. 


«r  surmounting  a  resistance,  by  being  placed  on  a  fulcrum, 
or  prop,  becomes  a  iever. 

284.  This  machine  is  the  most  simple  of  all  the  mechani- 
cal powers,  and  is  therefore  in  universal  use. 

285.  Fig.  40repre-         .  Fig.  40. 
«ents  a  straight  lever, 

or  handspike,  called 
also  a  crow-bar,  which 
is  commonly  used  in 
raising  and  moving 
stone  and  other  heavy 
bodies.  The  block  b 
is  the  weight,  or  re- 
sistance, a  is  the  lever,  and  c,  the  fulcrum. 

286.  The  power  is  the  hand,  or  weight  of  a  man,  applied 
at  a,  to  depress  that  end  of  the  lever,  and  thus  to  raise  the 
weight. 

It  will  be  observed,  that  by  this  arrangement,  the  applica- 
tion of  a  small  power  may  be  used  to  overcome  a  great  re- 
sistance. 

287.  The  force  to  be  obtained  by  the  lever,  depends  on  its 
length,  together  with  the  power  applied,  and  the  distance  of 
the  weight  and  power  from  the  fulcrum. 

288.  Suppose,  fig.  41,  that  a  Fig.  41. 
is  the  lever,  b  the  fulcrum,  d         ^ 

the  weight  to  be  raised,  and  c 
the  power.  Let  d  be  consider- 
ed three  times  as  heavy  as  c, 
and  the  fulcrum  three  times  as 
far  from  c  as  it  is  from  d ;  then 
the  weight  and  power  will  ex- 
actly balance  each  other.  Thus, 
if  the  bar  be  four  feet  long,  and  the  fulcrum  three  feet  from 
the  end,  then  three  pounds  on  the  long  arm,  will  weigh  just 
as  much  as  nine  pounds  on  the  short  arm,  and  these  pro- 
portions will  be  found  the  same  in  all  cases. 

289.  When  two  weights  balance  each  other,  the  fulcrum 

What  is  a  lever  1  What  is  the  simplest  of  all  mechanical  powers  1 
Explain  fig.  40.  Which  is  the  weight']  Where  is  the  fulcrum  1  Where 
is  the  power  applied"?  What  is  the  power  in  this  case?  On  what 
does  the  force  to  be  obtained  by  the  lever  depend  1  Suppose  a  lever  4 
feet  long,  and  the  fulcrum  one  foot  from  the  end,  what  number  of 
pounds  will  balance  each  other  at  the  ends  1  When  weights  balance 
each  other,  at  what  point  between  them  must  the  fulcrum  be? 


O 


6 


68  LEVER. 

is  always  at  the  centre  of  gravity  between  them,  and  there- 
fore, to  make  a  small  weight  raise  a  large  one,  the  fulcrum 
must  be  placed  as  near  as  possible  to  the  large  one,  since 
the  greater  the  distance  from  the  fulcrum  the  small  weight 
or  power  is  placed,  the  greater  will  be  its  force. 

290.  Suppose  me  weight  b,  Fig.  42. 
fig.  42,  to  be  sixteen  pounds, 

and  suppose  the  fulcrum  to  be 
placed  so  near  it,  as  to  be 
raised  by  the  power  a,  of  foury 
pounds,  hanging  equally  dis- 
tant from  the  fulcrum  and  the 
end  of  the  lever.  If  now  the 
power  a,  be  removed,  and 

another  of  two  pounds,  c,  be  placed  at  the  end  of  the  lever, 
its  force  will  be  just  equal  to  a,  placed  at  the  middle  of  the 
lever. 

291.  But  let  the  fulcrum  be  moved  along  to  the  middle  of 
the  lever,  with  the  weight  of  sixteen  pounds  still  suspended 
to  it,  it  would  then  take  another  weight  of  sixteen  pounds, 
instead  of  two  pounds,  to  balance  it,  fig.  43. 

292.  Thus,  the  power  which  Fig.  43. 

would    balance    16     pounds,         _ 

when  the  fulcrum  is  in  one 

place,  must  be  exchanged  for 
another  power  weighing  eight 
times  as  much,  when  the  ful- 
crum is  in  another  place. 

From   these  investigations, 
we  may  draw  the  following 

general  truth,  or  proposition,  concerning  the  lever :  "  That 
the  force  of  the  lever  increases  in  proportion  to  the  distance 
of  the  'power  from  the  fulcrum^  and  diminishes  in  pro- 
portion as  the  distance  of  the  weight  from  the  fulcrum  in- 
creases" 

293.  From  this  proposition  may  be  drawn  the  following 
rul<?,  by  which  the  exact  proportions  between  the  weight  or 
resistance,  and  the  power,  may  be  found.      Multiply  the 

Suppose  a  weight  of  16  pounds  on  the  short  arm  of  a  lever  is  coun- 
terbalanced by  4  pounds  in  the  middle  of  the  long  arm,  what  power 
wou'd  balance  this  weight  at  the  end  of  the  lever  1  Suppose  the  ful- 
crum to  be  moved  to  the  middle  of  the  lever,  what  power  would  then  be 
equ'M  to  16  pounds  ?  What  is  the  general  proposition  drawn  from 
Aiesrresults? 


LEVER. 


Fig.  44. 


weight  by  its  distance  from  thefulcium;  then  multiply  the 
•power  by  its  distance  from  the  same  point,  and  if  the,  pro- 
ducts are  equal,  the  weight  and  the  power  will  balance  each 
other. 

294.  Suppose  a  weight  of  100  pounds  on  the  short  arm 
of  a  lever,  8  inches  from  the  fulcrum,  then  another  weight, 
or  power,  of  8  pounds,  would  be  equal  to  this,  at  the  dis- 
tance of  100  inches  from  the  fulcrum ;  because  8  multiplied 
by  100  is  equal  to  800;  and   100  multiplied  by  8  is  equal 
to  800,  and  thus    they  would    mutually  counteract   each 
other. 

295.  Many  instruments 
in  common  use  are  on  the 
principle  of  this  kind  of  le- 
ver.      Scissors,    fig.    44, 
consist  of  two  levers,  the 
rivet  being  the  fulcrum  for 
both.    The  fingers  are  the 
power,  and  the  cloth  to  be 
cut,   the   resistance  to   be 
overcome. 

Pincers,  forceps,  and  sugar  cutters,  are  examples  of  this 
kind  of  lever. 

296.  A  common  scale-beam,  used  for  weighing,  is  a  lever, 
suspended  at  the  centre  of  gravity,  so  that  the  two  arms 
balance  each  other.  Hence  the  machine  is  called  a  balance. 
The  fulcrum,  or  what  is  called  the  pivot,  is  sharpened,  like 
a  wedge,  and  made  of  hardened  steel,  so  as  much  as  possi- 
ble to  avoid  friction. 

297.  A  dish  is  suspended  by  Fig.  45. 
cords  to  each  end  or  arm  of  the 

lever,  for  the  purpose  of  hold- 
ing the  articles  to  be  weighed. 
When  the  whole  is  suspended 
at  the  point  a,  fig.  45,  the  beam 
or  lever  ought  to  remain  in  a 
horizontal  position,  one  of  its 
ends  being  exactly  as  high  as  the  other.  If  the  weights  in 

What  is  the  rule  for  finding  the  proportions  between  the  weight  and 
\  ewer  1  Give  an  illustration  of  this  rule.  What  instruments  operate 
tm  the  principle  of  this  lever  1  When  the  scissors  are  used,  what  is 
the  resistance,  and  what  the  power  ?  In  the  common  scale-beam, 
where  is  the  fulcrum  1  In  what  position  ought  the  scale-beam  »* 
nang  ? 


70  LEVER* 

the  two  dishes  are  equal,  and  the  support  exactly  in  the  con 
tre,  they  will  always  hang  as  represented  in  the  figure. 

298.  A  very  slight  variation  of  the  point  of  support  to- 
wards one  end  of  the  lever,  will  make  a  difference  in  the 
weights  employed  to  balance  each  other.     In  weighing  a 
pound  of  sugar,  with  a  scale  beam  of  eight  inches  long,  if 
the  point  of  support  is  half  an  inch  too  near  the  weight,  the 
buyer  would  be  cheated  nearly  one  ounce,  and  consequently 
nearly  one  pound  in  every  sixteen  pounds.     This  fraud 
might  instantly  be  detected  by  changing  the  places  of  the 
sugar  and  weight,  for  then  the  difference  would  be  quite 
material,  since  the  sugar  would  then  seem  to  want  twice  as 
much  additional  weight  as  it  did  really  want. 

299.  The  steel-yard  differs  from  the  balance,  in  having 
its  support  near  one  end,  instead  of  in  the  middle,  and  also 
in  having  the  weights  suspended  by  hooks,  instead  of  being 
placed  in  a  dish. 

300.  If  we  suppose  the  beam  Fig.  46. 

to  be  7  inches    long,  and  the        ^    j  2    3     4    5    6 
hook,  c,  fig.  46,  to  be  one  inch  s-—l     \     r     i     j 
from  the  end,  then  the  pound   T^~~  tf 

weight  a,  will  require  an  addi-  Q 

tional  pound  at  b,  for  every  inch 
it  is  moved  from  it.  This,  how- 
ever,  supposes  that  the  bar  will 
balance  itself,  before  any  weights  are  attached  to  it. 

In  the  kind  of  lever  described,  the  weight  to  be  raised  is 
on  one  side  of  the  fulcrum,  and  the  power  on  the  other. 
Thus  the  fulcrum  is  between  the  power  and  the  weight. 

301.  There    is    an-  Fig.  47. 
other  kind  of  lever,  in 

the  use  of  which,   the 

weight    is    placed    be- 

tween the  fulcrum  and 

the    hand.       In    other 

words,  the  weight  to  be  J^  /"K 

lifted,  and  the  power  by          '        *— 

which  it  is  moved,  are 

on  the  same  side  of  the 

prop. 

302.  This  arrangement  is  represented  by  fig.  47,  where 

How  may  a  fraudulent  scale-beam  be  made  1  How  may  the  cheat 
be  detected  1  How  does  the  steel-yard  differ  from  the  balance  1 


^ 

s-—l 

T^~ 
V 

j\ 
*  —  * 


r 

fl 


LEVER. 


71 


w  is  the  weight,  I  the  lever,  /the  fulcrum,  and  p  a  pulley, 
over  which  a  string  is  thrown,  and  a  small  weight  suspend- 
ed, as  the  power.  In  the  common  use  of  a  lever  of  the 
first  kind,  the  force  is  gained  by  hearing  down  the  long 
arm  of  the  lever,  which  is  called  prying.  In  the  se- 
cond kind,  the  force  is  gained  by  carrying  the  long  arm  in 
a  contrary  direction,  or  upward,  and  this  is  called  lifting. 

303.  Levers  of  the  second  kind  are  not  so  common  as  the 
first,  but  are  frequently  used  for  certain  purposes.      The 
oars  of  a  boat  are  examples  of  the  second  kind.     The  water 
against  which  the  blade  of  the  oar  pushes,  is  the  fulcrum, 
the  boat  is  the  weight  to  be  moved,  and  the  hands  of  the 
iian  the  power. 

304.  Two  men  carrying  a  load  between  them  on  a  pole, 
is  also  an  example  of  this  kind  of  lever.     Each  man  acts  as 
the  power  in  moving  the  weight,  and  at  the  same  time  each 
becomes  the  fulcrum  in  respect  to  the  other. 

If  the  weight  happens  to  slide  on  the  pole,  the  man  to- 
wards whom  it  goes,  has  to  bear  more  of  it  in  proportion  as 
its  distance  from  him  is  less  than  before. 

305.  A  load  at  a,  fig.  48,  is 
borne  equally  by  the  two  men, 
being    equally   distant    frora 
each  other ;    but  at  b,  three 
quarters  of  its  weight  would 
be  on  the  man  at  that  end,  be- 
cause   three   quarters  of  the 

length  of  the  lever  would  be  on  the  side  of  the  other  man. 


306.  In  the  third,  and  last 
kind  of  lever,  the  weight  is 
placed  at  one  end,  the  ful- 
crum at  the  other  end,  and 
the  power  between  them,  or 
the  hand  is  between  the  ful- 
crum and  the  weight  to  be 
lifted. 

307.  This  is  represented 
by  fig.   49,  where  c  is  the 


Fig.  49. 


In  the  first  kind  of  lever,  where  is  the  fulcrum,  in  respect  to  the 
weight  and  power  ]  In  the  second  kind,  where  is  the  fulcrum,  in  re- 
spect to  the  weight  and  power  ?  What  is  the  action  of  the  first  kind 
called  1  What  is  the  action  of  the  second  kind  called  1  Give  exam- 
ples of  the  second  kind  of  lever.  In  rowing  a  boat,  what  is  the  fulcrum, 
what  the  weight,  and  what  the  power  1  What  other  illustrations  of 
this  principle  is  given  1  In  the  third  kind  of  lever,  where  are  the  re- 
spective phr.es  of  the  weight,  power,  and  fulcrum  1 


72 


LEVER. 


fulcrum,  a  the  power,  suspended  over  the  pulley  b,  and 
d  is  the  weight  to  be  raised. 

308.  This  kind  of  lever  works  to  great  disadvantage,  since 
the  power  must  be  greater  than  the  weight.    It  is  therefore 
seldom  used,  except  in  cases  where  velocity  and  not  force  is  re- 
quired.    In  raising  a  ladder  from  the  ground  to  the  roof  of  a 
house,  men  are  obliged  sometimes  to  make  use  of  this  prin- 
ciple, and  the  great  difficulty  of  doing  it,  illustrates  the  me 
chanical  disadvantage  of  this  kind  of  lever. 

309.  We  have  now  described  three  kinds  of  levers,  and, 
we  hope,  have  made  the  manner  in  which  each  kind  acts 
plain,  by  illustrations.     But  to  make  the  difference  between 
them  still  more  obvious,  and  to  avoid  all  confusion,  we  will 
here  compare  them  together. 

310.  In  the  first  kind,  the  weight,  or  resistance,  is  on  the 
short  arm  of  the  lever,  the  power,  or  hand,  on  the  long  arm, 
and  the  fulcrum  between  them.     In  the  second  kind,  the 
weight  is  between  the  fulcrum  and  the  hand,  or  power;  and, 
in  the  third  kind  the  hand  is  between  the  fulcrum  and  tha 
weight. 

Fig.  50. 


311.  In  fig.  50,  the  weight  and  hand  both  act  downwards. 
In  51,  the  weight  and  hand  act  in  contrary  directions*,  the 

What  is  the  disadvantage  of  this  kind  of  lever  1  Give  an  example 
of  the  use  of  the  third  kind  of  lever.  In  what  direction  do  the  hand 
and  weight  act,  in  the  first  kind  of  lever  *?  In  what  direction  do  they  act 
in  the  second  kind  1  In  what  direction  do  they  act  in  the  third  kindl 


LEVER.  73 

hand  upwards  and  the  weight  downwards,  the  weight  being 
between  them.  In  52,  the  hand  and  weight  also  act  in  con- 
trary directions,  but  the  hand  is  between  the  fulcrum  and 
the  weight. 

312.  Compound  Lever. — When  several  simple  levers  are 
connected  together,  and  act  one  upon  the  other,  the  machine 
is  called  a  compound  lever.  In  this  machine,  as  each  lever 
acts  as  an  individual,  and  with  a  force  equal  to  the  action  of 
the  next  lever  upon  it,  the  force  is  increased  or  diminished, 
and  becomes  greater  or  less,  in  proportion  to  the  number  or 
kind  of  levers  employed. 

We  will  illustrate  this  kind  of  lever  by  a  single  example, 
but  must  refer  the  inquisitive  student  to  more  extended 
works  for  a  full  investigation  of  the  subject. 

313.  Fig.  Fig.  53. 
53,    repre- 

sents         a  <;  Y    .•         . . 

compound  A 

lever,   con- 
sisting of  3  J 
simple    le-(_)# 
vers  of  the 
first  kind. 

314.  In  calculating  the  force  of  this  lever,  the  rule  ap- 
plies, which  has  already  been  given  for  the  simple  lever, 
namely,  the  length  of  the  long  arm  is  to  be  multiplied  by  the 
moving  power,  and  that  of  the  short  one,  by  the  weight,  or 
resistance.     Let  us  suppose,  then,  that  the  three  levers  in  the 
figure  are  of  the  same  length,  the  long  arms  being  six 
inches,  and  the  short  ones,  two  inches  long;  required,  the 
weight  which  a  moving  power  of  1  pound  at  a  will  balance 
at  b.     In  the  first  place,   1   pound  at  a,  would  balance  3 
pounds  at  e,  for  the  lever  being  6  inches,  and  the  power  1 
pound,  6X1=6,  and  the  short  one  being  2  inches,  2X3=6. 
The  long  arm  of  the  second  lever  being  also  6  inches,  and 
moved  with  a  power  of  3  pounds,  multiply  the  3  by  6—18; 
and  multiply  the  length  of  the  short  arm,  being  2  inches, 
by  9=18.     These  two  products  being  equal,  the  power  upon 
the  long  arm  of  the  third  lever,  at  d,  would  be  9  pounds. 
9  poundsX6=54,  and  27X2,  is  54;  so  that  one  pound  at  a 
would  balance  27  at  b. 

What  is  a  compound  lever  1  By  what  rule  is  the  force  of  the  com- 
pound lever  calculated  7  How  many  pounds  weight  will  be  raised  by 
three  levers  connected,  of  eight  inches  each,  with  the  fulcrum  two 
inches  from  the  end,  by  a  power  of  one  pound  1 


74  WHEEL  AND  AXLE. 

The  increase  offeree  is  thus  slow,  because  the  proportion 
Between  the  long  and  short  arms,  is  only  as  2  to  6,  or  in  the 
proportions  ol  1,  3,  9. 

315.  Now  suppose  the  long  arms  of  these  levers  to  be  18 
inches,  and  the  short  ones   1  inch,  and  the  result  will  be 
surprisingly  different,  for  then  1  pound  at  a  would  balance 
18  pounds  at  e,  and  the  second  lever  would  have  a  power 
of  18  pounds.     This  being  multiplied  by  the  length  of  the 
lever,  18X18=324  pounds  at  d.    The  third  lever  would  thus 
be  moved  by  a  power  of  324  pounds,  which,  multiplied  by  18 
inches  for  the  weight  it  would  raise,  would  give  5832  pounds. 

The  compound  lever  is  employed  in  the  construction  of 
weighing  machines,  and  particularly  in  cases  where  great 
weights  are  to  be  determined,  in  situations  where  other  ma- 
chines would  be  inconvenient,  on  account  of  their  occupying 
too  much  space. 

WHEEL  AND  AXLE. 

316.  The  mechanical  power,  next  to  the  lever  in  sim- 
plicity, is  the  wheel  and  axle.     It  is,  however,  much  more 
complex  than  the  lever.     It  consists  of  two  wheels,  one  of 
which  is  larger  than  the  other,  but  the  small  one  passes 
through  the  larger,  and  hence  both  have  a  common  centre, 
on  which  they  turn. 

317.  The  manner  in  which  Fig.  54. 
this  machine  acts,  will  be  un- 
derstood by  fig.  54.  The  large 

wheel  a,  on  turning  the  ma- 
chine, will  take  up,  or  throw 
off^  as  much  more  rope  than 
the  small  wheel  or  axle  b,  as 
its  circumference  is  greater. 
If  we  suppose  the  circumfer- 
ence of  the  large  wheel  to  be 
four  times  that  of  the  small 
one,  then  it  will  take  up  the 
rope  four  times  as  fast.  And 
because  a  is  four  times  as  large  as  b,  1  pound  at  d  will  bai 
ance  4  pounds  at  c,  on  the  opposite  side. 

If  the  long  arms  of  the  levers  be  18  inches,  and  the  short  one  on» 
inch,  how  much  will  a  power  of  one  pound  balance  1  In  what  ma* 
chines  is  the  compound  lever  employed  1  What  advantages  do  these 
machines  possess  over  others  ?  What  is  the  next  simple  mechanical 
power  to  the  lever  1  Describe  this  machine  1  Explain  fig.  54.  On  what 
principle  does  this  machine  act  7 


WHEEL  AND  AXLE.  75 

318.  The  principle  of  this  machine  is  that  of  the  .ever, 
as  will  be  apparent  by  an  examination  of  fig.  55. 

319.  This  figure  represents  the  ma-  Fig.  55. 
chine  endwise,  so  as  to  show  in  what 

manner  that  lever  operates.  The  two 
weights  hanging  in  opposition  to  each 
other,  the  one  on  the  wheel  at  a,  and 
the  other  on  the  axle  at  b,  act  in  the 
same  manner  as  if  they  were  connected 
by  the  horizontal  lever  a  b,  passing 
from  one  to  the  other,  having  the  com- 
mon centre,  c,  as  a  fulcrum  between 
them. 

320.  The  wheel  and  axle,  therefore, 
acts  like  a  constant  succession  of  levers, 

the  long  arm  being  half  the  diameter  of  the  wheel,  and  the 
short  one  half  the  diameter  of  the  axle  ;  the  common  cen- 
tre of  both  being  the  fulcrum.  The  wheel  and  axle  has, 
therefore,  been  called  the  perpetual  lever. 

321.  The  great  advantage  of  this  mechanical  arrange- 
ment is,  that  while  a  lever  of  the  sume  power  can  raise  a 
weight  but  a  few  inches  at  a  time,  and  then  only  in  a  cer- 
tain direction,  this  machine  exerts  a  continual  force,  and  in 
any  direction  wanted.     To  change  the  direction,  it  is  only 
necessary  that  the  rope  by  whif.n  the  weight  is  to  be  raised, 


should  be  carried  in 
a  line  perpendicular 
to  the  axis  of  the  ma- 
chine, to  the  place  be- 
low which  the  weight 
lies,  and  there  be  let 
fall  over  a  pulley. 

322.  Suppose  the 
wheel  and  axle,  fig. 
56,  is  erected  in  the 
third  story  of  a  store 
house,  with  the  axle 
over  the  scuttles,  or 
doors  through  the 


Fig.  56. 


In  fig.  55,  which  is  the  fulcrum.,  and  which  the  two  arms  of  the  lever  l 
What  is  this  machine  called,  in  reference  to  the  principle  on  which  i ' 
acts  1  What  is  the  great  advantage  of  this  machine  over  the  lever  am 
other  mechanical  powers  7    Describe  fig.  56.  and  point  out  the  mam  )" 
in  which  weights  can  be  raised  by  letting  fail  a  rope  over  the  puiiey- 


WHEEL  AND  AXLE. 


floors,  so  that  goods  can  be  raised  by  it  from  the  ground 
floor,  in  the  direction  of  the  weight  a.  Suppose,  also,  that 
the  same  store  stands  on  a  wharf,  where  ships  come  up  to 
>ts  side,  and  goods  are  to  be  removed  from  the  vessels  into 
the  upper  stories.  Instead  of  removing  the  goods  into  the 
saore,  and  hoisting  them  in  the  direction  of  a,  it  is  only  ne- 
cessary to  carry  the  rope  b,  over  the  pulley  c,  which  is  at 
the  end  of  a  strong  beam  projecting  out  from  the  side  of  the 
store,  and  then  the  goods  will  be  raised  in  the  direction  of  d, 
thus  saving  the  labour  of  moving  them  twice. 

The  wheel  and  axle,  under  different  forms?  is  applied  to  a 
variety  of  common  purposes. 

323.  The  capstan,  in  universal  Fig.  57. 
use,  on  board  of  ships  and  other 

vessels,  is  an  axle  placed  upright, 
with  a  head,  or  drum,  a,  fig.  57, 
pierced  with  holes,  for  the  levers 
b,  c,  d.  The  weight  is  drawn  by 
the  rope  e,  passing  two  or  three 
times  round  the  axle  to  prevent  its' 
slipping. 

This  is  a  very  powerful  and 
convenient  machine.  When  not  in  use,  the  levers  are  taken 
out  of  their  places  and  laid  aside,  and  when  great  force  is 
required,  two  or  three  men  can  push  at  each  lever. 

324.  The  common  windlass  for  drawing  water,  is  another 
modification  of  the  wheel  and  axle.     The  winch,  or  crank, 
by  which  it  is  turned,  is  moved  around  by  the  hand,  and 
there  is  no  difference  in  Fig.  58. 

the  principle,  whether         [^ffTtrTTt 
a  whole  wheel  is  turn-      r= 
ed,  or  a  single  spoke.  |flJJUU.a-& 

The  winch,  therefore, 
answers  to  the  wheel,  "^ 
while  the  rope  is  taken 
up,  and  the  weight  rais- 
ed by  the  axle,  as  al- 
ready described. 

325.  In  cases  where 

great  weights  are  to  be  raised,  and  it  is  required  that  the 
machine  should  be  as  small  as  possible,  on  account  of  room, 

What  is  the  capstan  1  Where  is  it  chiefly  used  1  What  are  the  pe- 
culiar advantages  of  this  form  of  the  wheel  and  axlel  In  the  com- 
mon windlass,  what  part  answers  to  the  wheel  1  Explain  fig.  58. 


*.  iSJliaJ3 


WHEEL  AND  AXLE.  77 

the  simple  wheel  and  axle,  modified  as  represented  by  fig. 
58,  is  sometimes  used. 

326.  The  axle  may  be  considered  in  two  parts,  one  of 
which  is  larger  than  the  other.     The  rope  is  attached  by 
its  two  ends,  to  the  ends  of  the  axle,  as  seen  in  the  figure. 
The  weight  to  be  raised  is  attached  to  a  small  pulley,  or 
wheel,  round  which  the  rope  passes.     The  elevation  of  the 
weight  may  be  thus  described.     Upon  turning  the  axle,  the 
rope  is  coiled  round  the  larger  part,  and  at  the  same  time  it 
is  thrown  off  the  smaller  part.     At  every  revolution,  there- 
fore, a  portion  of  the  rope  will  be  drawn  up,  equal  to  the 
circumference  of  the  thicker  part,  and  at  the  same  time  a 
portion,  equal  to  that  of  the  thinner  part,  will  be  let  down. 
On  the  whole,  then,  one  revolution  of  th£  machine  will 
shorten  the  rope  where  the  weight  is  suspended,  ju3t  as 
much  as  the  difference  between  the  circumference  of  the 
two  parts. 

327.  Now,  to  understand  the  principle  on 
which  this  machine  acts,  we  must  refer  to 
fig.  59,  where  it  is  obvious  that  the  two 
parts  of  the  rope  a  and  b,  equally  support, 
the  weight  d,  and  that  the  rope,  as  the  ma- 
chine turns,  passes   from  the  small  part  of 
the  axle  e,  to  the  large  part  h,  consequently, 
the  weight  does  not  rise  in  a  perpendicular 
line  towards  e,  the  centre  of  both,  but  in  a 
line  between  the  outsides  of  the  large  and 
small  parts.     Let  us  consider  what  would 
be  the  consequence  of  changing  the  rope  a 
to  the  larger  part  of  the  axle,  so  as  to  place 
the  weight  in  a  line  perpendicular  to  the 

axis  of  motion.  In  this  case,  it  is  obvious  that  the  machine 
would  be  in  equilibrium,  since  the  weight  d  would  be  di- 
vided between  the  two  sides  equally,  and  the  two  arms  of  a 
lever  passing  through  the  centre  c,  would  be  of  equal  length, 
and  therefore  no  advantage  would  be  gained.  But  in  the 
actual  arrangement,  the  weight  being  sustained  equally  by 
the  large  and  small  parts,  there  is  involved  a  lever  power, 
the  long  arm  of  which  is  equal  to  half  the  diameter  of  the 

Why  is  the  rope  shortened,  and  the  weight  raised  ?  What  is  the  de- 
sign of  fig.  59  1  Does  the  weight  rise  perpendicular  to  the  axis  of  mo- 
tion ]  Suppose  the  cylinder  was,  throughout,  of  the  same  size,  what 
would  be  the  consequence  1  On  what  principle  does  this  machine  act  7 
Which  are  the  long  and  short  arms  of  the  lever,  and  where  is  the  ful- 


78  WHEEL  AND  AXLE. 

large  part,  while  the  short  arm  is  equal  to  half  the  diameter 
of  the  small  part,  the  fulcrum  being  between  them. 

328.  System  of  Wheels. — As  the  wheel  and  axle  is  only 
a  modification  of  the  simple  lever,  so  a  system  of  wheels 
acting  on  each  other,  and  transmitting  the  power  to  the  re- 
sistance, is  only  another  form  of  the  compound  lever. 

329.  Such  a  combi- 
nation is  shown  in  fig. 
60.     The  first  wheel, 
a,   by   means   of  the 
teeth,  or  cogs,  around 
its  axle,  moves  the  se- 
cond wheel,  b,  with  a 
force  equal  to  that  of 
a  lever,  the  long  arm 
of  which  extends  from 
the  centre  of  the  wheel 
and  axle   to  the   cir- 
cumference    of     the 
wheel,  where  the  pow- 
er p  is  suspended,  and  the  short  pjrn  from  the  same  centre 
to  the  ends  of  the  cogs.     The  dotted  line  c,  passing  through 
the  centre  of  the  wheel  a,  shows  the  position  of  the  lever, 
as  the  wheel  now  stands.      The    centre    on   which  both 
wheels  turn,  it  will  be  obvious,  is  the  fulcrum  of  this  lever. 
As  the  wheel  turns,  the  short  arm  of  this  lever  will  act  upon 
the  long  arm  of  the  next  lever  by  means  of  the  teeth  on  the 
circumference  of  the  wheel  b,  and  this  again  through  the 
teeth  on  the  axle  of  A,  will  transmit  its  force  to  the  circurr 
ference  of  the  wheel  d,  and  so  by  the  short  arm  of  the  third 
lever  to  the  weight  w.     As  the  power  or  small  weight  falls 
therefore,  the  resistance,  w,  is  raised,  with  the  multiplied 
force  of  three  levers,  acting  on  each  other. 

330.  In  respect  to  the  force  to  be  gained  by  such  a  ma 
chine,  suppose  the  number  of  teeth  on  the  axle  of  the  wheel 
a,  to  be  six  times  less  than  the  number  of  those  on  the  cir- 
cumference *of  the  wheel  b,  then  b  would  only  turn  round 
once,  while  a  turned  six  times.     And,  in  like  manner,  if 
the  number  of  teeth  on  the  circumference  of  d,  be  six  times 
greater  than  those  on  the  axle  of  b,  then  d  would  turn  once, 


)n  what  principle  does  a  system  of  wheels  act,  as  represented  in  fig, 
60  7  Explain  fig.  60,  and  show  how  the  power  p  is  transferred  by  the 
action  of  levers  to  w. 


WHEEL  AND  AXLE.  79 

«viiile  b  turned  six  times.  Thus,  six  revolutions  of  a  would 
make  b  revolve  once,  and  six  revolutions  of  b  would  make 
d  revolve  once.  Therefore,  a  makes  thirty-six  revolutions 
while  d  makes  only  one. 

331.  The  diameter  of  the  wheel  a,  being  three  times  the 
diameter  of  the  axle  of  the  wheel  d,  and  its  velocity  of  mo- 
tion being  36  to  1,  3  times  36  will  give  the  weight  which 
a  power  of  1  pound  at  p  would  raise  at  w.  Thus  36X3=108. 
One.  pound  at  p  would  therefore  balance  108  pounds  at  w. 

332.  No  machine  creates  force. — If  the  student  has  attend- 
ed closely  to  what  has  been  said  on  mechanics,  he  will  now 
be  prepared  to  understand,  that  no  machine,  however  simple 
or  complex  it  may  be,  can  create  the  least  degree  of  force. 
It  is  true,  that  one  man  with  a  machine,  may  apply  a  force 
Avhich  a  hundred  could  not  exert  with  their  hands,  but  then 
it  would  take  him  a  hundred  times  as  long. 

333.  Su  ppose  there  are  twenty  blocks  of  stone  to  be  moved 
a  hundred  feet  ;*  perhaps  twenty  men,  by  taking  each  a 
block,  would  move  them  all  in  a  minute.     One  man,  with  a 
capstan,  we  will  suppose,  may  move  them  all  at  once,  but 
this  man,  with  his  lever,  would  have  to  make  one  revolution 
for  every  foot  he  drew  the  whole  load  towards  him,  and 
therefore  to  make  one  hundred  revolutions  to  perform  the 
whole  work.     It  would  also  take  him  twenty  times  as  long 
to  do  it,  as  it  took  the  twenty  men.   His  task,  indeed,  would 
be  more  than  twenty  times  harder  than  that  performed  by 
the  twenty  men,  for,  in  addition  to  moving  the  stone,  he 
would  have  the  friction  of  the  machinery  to  overcome,  which 
commonly  amounts  to  nearly  one  third  of  the  force  em- 
ployed. 

334.  Hence  there  would  be  an  actual  loss  of  power  by 
the  use  of  the  capstan,  though  it  might  be  a  convenience  for 
the  one  man  to  do  his  work  by  its  means,  rather  than  to 
call  in  nineteen  of  his  neighbours  to  assist  him. 

335.  The  same  principle  holds  good  in  respect  to  other 
machinery,  where  the  strength  of  man  is  employed  as  the 
power,  or  prime  maver.      There  is  no  advantage  gained, 
except  that  of  convenience.     In  the  use  of  the  most  simple 
of  all  machines,  the  lever,  and  where,  at  the  same  time,  there 

What  weight  will  one  pound  at  p  balance  at  w  1  Is  there  any  actual 
power  gained  by  the  use  of  machinery  1  Suppose  20  men  to  move  20 
stones  to  a  certain  distance  with  their  hands,  and  one  man  moves 
them  back  to  the  same  place  with  a  capstan,  which  performs  the  most 
actual  labour  ?  Why  1  Why,  then,  is  machinery  a  convenience  1 


SO  WHEEL  AND  AXLE. 

is  the  least  force  lost  by  friction,  there  is  no  actual  gain  of 
Dower,  for  what  seems  to  be  gained  in  force  is  always  lost 
in  velocity.  Thus,  if  a  lever  is  of  such  length  to  raise  100 
pounds  an  inch  by  the  power  of  one  pound,  its  long  arm 
must  pass  through  a  space  of  100  inches.  Thus,  what  is 
gained  in  one  way  is  lost  in  another. 

336.  Any  power  by  which  a  machine  is  moved,  must  be 
equal  to  the  resistance  to  be  overcome,  and,  in  all  cases 
where  the  power  descends,  there  will  be  a  proportion   be- 
tween the  velocity  with  which  it  moves  downwards,  and  the 
velocity  with   which  the  weight  moves  upwards.     There 
will  be  no  difference  in  this  respect,  whether  the  machine  be 
simple  or  compound,  for  if  its  force  be  increased  by  increasing 
the  number  of  levers,  or  wheels,  the  velocity  of  the  moving 
power  must  also  be  increased,  as  that  of  the  resistance  is 
diminished. 

337.  There  being,  then,  always  a  proportion,  between  the 
velocity  with  which  the  moving  force  descends,  and  that 
with  which  the  weight  ascends,  whatever  this  proportion 
may  be,  it  is  necessary  that  the  power  should  have  to  the 
resistance  the  same  ratio  that  the  velocity  of  the  resistance 
has  to  the  velocity  of  the  power.     In  other  words,  "  The 
power  multiplied  by  the  space  through  which  it   moves,  in 
a  vertical  direction,  must  be  equal  to  the  weight  multiplied 
by  the  space  through  which  it  moves  in  a  vertical  direc- 
tion" 

338.  This  law  is  known  under  the  name  of  "  the  law  of 
virtual  velocities,"  and  is  considered  the  golden  rule  of 
mechanics. 

339.  This  principle  has  already  been  explained,  while 
treating  of  the  lever  (292) ;  but  that  the  student  should  want 
nothing  to  assist  him  in  clearly  comprehending  so  import- 
ant a  law,  we  will  again  illustrate  it  in  a  different  manner. 

340.  Suppose  the  weight  of  ten  pounds  to  be  suspended 
on  the  short  arm  of  the  lever,  fig.  61,  and  that  the  ful- 
crum is  only  one  inch  from  the   weight ;  then,   if  the  le- 

In  the  use  of  the  lever,  what  proportion  is  there  between  the  force 
of  the  short  arm,  and  the  velocity  of  the  long  arm  1  How  is  this  illus- 
trated 1  It  is  said,  that  the  velocity  of  the  power  downwards,  must 
be  in  proportion  to  that  of  the  weight  upwards  1  Does  it  make  any  dif- 
ference, in  this  respect,  whether  the  machine  be  simple  or  compound  1 
What  is  the  golden  rule  of  mechanics'?  Under  wha't  name  is  this  law 
known  1 


WHEEL  AND  AXLE. 


81 


ver  be  ten  inches  long,  on  the  other  side          Fig.  61. 

of  the  fulcrum,  one  pound  at  a  would  raise, 

or  balance,  the  ten  pounds  at  b.     But  in 

raising  the  ten  pounds  one  inch  in  a  ver-  > 

tical  direction,  the  long  arm  of  the  lever 

must  fall  ten  inches  in  a  vertical  direction, 

and  therefore  the  velocity  of  a  would  be 

ten  times  the  velocity  of  b, 

341.  The  application  of  this  law,  or 

rule,  is  apparent.  The  power  is  one  pound,  and  the  space 
through  which  it  falls  is  ten  inches,  therefore  10X1=10. 
The  weight  is  10  pounds,  and  the  space  through  which  it 
rises  is  one  inch,  therefore  1X10=10. 

342.  Thus,  the  power,  multiplied  by  the  space  through 
which  it  moves,  is  exactly  equal  to  the  weight,  multiplied 
by  the  space  through  which  it  moves. 


Fig.  62. 


343.  Again,  suppose  the 
lever,  fig.  62,  to  be  thirty 
inches  long  from  the  ful- 
crum to  the  point  where 
the  power  p  is  suspended, 
and  that  the  weight  w  is 
two  inches  from  the  ful- 
crum. If  the  power  be  1 
pound,  the  weight  must  be 
15  pounds,  to  produce  equi- 
librium, and  the  power  p 
must  fall  thirty  inches,  to, 
raise  the  weight  w  2  inch- 
es. Therefore  the  power 
being  one  pound,  and  the  space  30  inches,  30X1=30.  The 
weight  being  15  pounds,  and  the  space  2  inches,  15X2=30. 

Thus,  the  power,  multiplied  by  the  space  through  which 
it  falls,  and  the  weight  multiplied  by  the  space  through 
which  it  rises,  are  equal. 

However  complex  the  machine  may  be,  by  which  the 
force  of  a  descending  power  is  transmitted  to  the  weight  to 
be  raised,  the  same  rule  will  apply,  as  it  does  to  the  action 
of  the  simple  lever. 

Explain  fig.  61,  and  show  how  the  rule  is  illustrated  by  that  figure. 
Explain  fig.  62,  and  show  how  the  same  rule  is  illustrated  by  it.  What 
is  said  of  the  application  of  this  rule  to  complex  machines  ? 


82 


PULLET. 


Fig.  63. 


THE  PULLEY. 

344.  A  pulley,  consists  of  a  wheel,  which  is  grooved  on 
the  edge,  and  which  is  made  to  turn  on  its  axis,  by  a  chorfc 
passing  over  it. 

345.  Fig.   63  represents    a  simple 
pulley,  with  a  single  fixed  wheel.     In 
other  forms  of  the  machine,  the  wheel 
moves  up  and  down,  with  the  weight. 

346.  The  pulley  is  arranged  among 
the  simple  mechanical  powers  ;    but 
when  several  are  connected,  the  ma- 
chine is  called  a  system  of  pulleys,  or 
a  compound  pulley. 

347.  One  of  the  most  obvious  ad- 
vantages of  the  pulley  is,  its  enabling 

men  to  exert  their  own  power,  in  places  where  they  cannot 
go  themselves.  Thus,  by  means  of  a  rope  and  wheel,  a 
man  can  stand  on  the  deck  of  a  ship,  and  hoist  a  weight  to 
the  topmast. 

By  means  of  two  fixed  pulleys,  a  weight  may  be  raised 
upward,  while  the  power  moves  in  a  horizontal  direction. 
The  weight  will  also  rise  vertically  through  the  same  space 
that  the  rope  is  drawn  horizontally. 

348.  Fig.    64    represents 
two  fixed  pulleys,  as  they  are 
a'/ranged  for  such  a  purpose. 
In  the  erection  of  a  lofty  edi- 
fice, suppose  the  upper  pulley 
to  be  suspended  to  some  part 
of  the  building  ;  then  a  horse, 
pulling  at  the   rope  a,  would 
raise  the  weight  w  vertically, 
as   far  as   he   went    horizon- 
tally. 

349.  In   the   use    of   the 
wheel  of  the  pulley,  there  is 

no  mechanical  advantage,  except  that  which  arises  from  re- 
moving the  friction,  and  diminishing  the  imperfect  flexibi- 
ity  of  the  rope. 

What  is  a  pulley  1  What  is  a  simple  pulley  1  What  is  a  system 
of  pulleys,  or  a  compound  pulley  *?  .  What  is  the  most  obvious  advan- 
tage of  the  pulley  1  How  must  two  fixed  pulleys  be  placed  to  raise  a 
•weight  vertically,  as  far  as  the  power  goes  horizontally  1  What  is 
ht  advantage  of  the  wheel  of  the  pulley  7 


Fig.  64. 


S~\ 


PULLET. 


83 


350.  hi  the  mechanical  effects  of  this  machine,  the  result 
would  be  the  same,  did  it  slide  on  a  smooth  surface  with  the 
same  ease  that  its  motion  makes  the  wheel  revolve. 

351.  The  action  of  the  pulley  is  on  a  different  principle 
from  that  of  the  wheel  and  axle.     A  system  of  wheels,  as 


Fig.  G5. 


already  explained,  acts  on  the  same  prin- 
ciple  as  the  compound  lever.  But  the 
mechanical  efficacy  of  a  system  of  pul- 
leys, is  derived  entirely  from  the  division 
of  the  weight  among  the  strings  employed 
in  suspending  it.  In  the  use  of  the  single 
fixed  pulley,  there  car.  be  no  mechanical 
advantage,  since  the  weight  rises  as  fast  as 
the  power  descends.  This  is  obvious  by 
fig.  63  ;  where  it  is  also  apparent  that  the 
power  and  weight  must  be  exactly  equal, 
to  balance  each  other. 

352.  In  the  single  moveable  pulley,  fig.  65, 
the  same  rope  passes  from  the  fixed  point  a, 
to  the  power  p.      It  is  evident  here,  that  the 
weight  is  supported  equally  by  the  two  parts 
of  the  string  between  which  it  hangs.    There- 
fore, if  we  call  the  weight  w  ten  pounds,  five 
pounds  will  be  supported  by  one  string,  and 
five  by  the  other.     The  power,  then,  will  sup- 
port twice  its  own   weight,  so  that  a  person 
pulling  with  a  force  of  five  pounds  at  p,  will 
raise  ten  pounds  at  w.     The  mechanical  force, 
therefore,  in  respect  to  the  power,  is  as  two  to 
one. 

In  this  example,  it  is  supposed  there  are  only 
two  ropes,  each  of  which  bears  an  equal  part 
of  the  weight. 

353.  If  the  number  of  ropes  be  increased, 
the  weight  may  be  increased  with  the  same 
power;  or  the  power  may  be  diminished  in 
proportion  as  the  number  of  ropes  is  increas- 
ed.    In  fig.  66,  the  number  of  ropes  sustain- 
ing  the  weight  is  four,   and   therefore,    the 
weight  may  be  four  times  as  great  as  the  power. 


How  does  the  action  of  the  pulley  differ  from  that  of  the  wheel  and 
axle  ?  Is  there  any  mechanical  advantage  in  the  fixed  pulley  '*  What 
weight  atp,  fig.  65,  will  balance  ten  pounds  at  w  7  Suppose  the  num- 
ber of  ropes  be  increased,  and  the  weight  increased,  must  the  power  bo 
increased  also  7 


r»4  PULLEY. 

Tills  principle  must  be  evident,  since  it  is  plain  that  each 
rope  sustains  an  equal  part  of  the  weight.  The  weight 
may  therefore  be  considered  as  divided  into  four  parts,  and 
each  part  sustained  by  one  rope. 

354.  In  fig.  67,  there  is  a  system  of  pulleys  represented, 
in  which  the  weight  is  sixteen  times  the  power. 

.355.  The  tension  of  the  rope  Fig.  67. 

d,  e,  is  evidently  equal  to  the' 
power,  p,  because  it  sustains  it : 
d,  being  a  moveable  pulley,  must 
sustain  a  weight  equal  to  twice 
the  power ;  but  the  weight  which 
it  sustains,  is  the  tension  of  the 
second  rope,  d,  c.  Hence  the  ten- 
sion of  the  second  rope  is  twice 
that  of  the  first,  and,  in  like 
manner,  the  tension  of  the  third 
rope  is  twice  that  of  the  second, 
and  so  on,  the  weight  being  equal 
to  twice  the  tension  of  the  last 
rope. 

356.  Suppose  the  weight «?,  to 
be  sixteen  pounds,  then  the  two 
ropes,   8  and  8,  would   sustain 
just  8  pounds  each,  this  being  g 
the  whole  weight  divided  equally 
between  them.      The   next  two 
ropes,  4  and  4,  would  evidently 
sustain     but     half    this    whole, 

weight,  because  the  other  half  is  already  sustained  by  a 
rope,  fixed  at  its  upper  end.  The  next  two  ropes  sustain 
but  half  of  4,  for  the  same  reason-;  and  the  next  pair,  1  and 
1,  for  the  same  reason,  will  sustain  only  half  of  2.  Lastly, 
the  power  p,  will  balance  two  pounds,  because  it  sustains 
but  half  this  weight,  the  other  half  being  sustained  by  the 
same  rope,  fixed  at  its  upper  end. 

357.  It  is  evident,  that  in  this  system,  each  rope  and  pul- 
ley which  is  added,  will  double  the  effect  of  the  whole. 
Thus,  by  adding  another  rope  and  pulley  beyond  8,  the 

Suppose  the  weight,  fig.  66,  to  be  32  pounds,  what  will  each  rope 
bear  1  Explain  fig.  67,  and  show  what  part  of  the  weight  each  rope 
sustains,  and  why  1  pound  atp  will  balance  16  pounds  at  w.  Explain 
the  reason  why  each  additional  rope  and  pulley  will  double  the  effect 
of  the  whole,  or  why  its  weight  may  be  double  by  that  of 'all  the  others, 
with  the  same  power. 


W 


INCLINED  PLANE.  85 

weight  w  might  be  32  pounds,  instead  of  16,  and  still  be 
balanced  by  the  same  power. 

358.  In  our  calculations  of  the  effects  of  pulleys,  we  have 
allowed  nothing  for  the  weight  of  the  pulleys  themselves,  or 
for  the  friction  of  the  ropes.     In  practice,  however,  it  will 
be  found,  that  nearly  one  third  must  be  allowed  for  friction, 
and  that  the  power,  therefore,  to  actually  raise  the  weight, 
must  be  about  one  third  greater  than  has  been  allowed. 

359.  The  pulley,  like  other  machines,  obeys  the  laws  of 
virtual  velocities,  already  applied  to   the  lever  and  wheel. 
Thus,  "  in  a  system  of  pulleys,  the  ascent  of  the  weight,  or  re- 
sistance, is  as  much  less  than  the  descent  of  the  power,  as  the 
weight  is  greater  than  the  power}1    If,  as  in  the  last  example, 
the  weight  is  16  pounds,  and  the  power  1  pound,  tb^  weight 
will  rise  only  one  foot,  while  the  power  descends  16  feet. 

360.  In  the  single  fixed  pulley,  the  weight  and  power  are 
equal,  and,  consequently,  the  weight  rises  as  fast  as  the 
power  descends. 

361.  With  such  a  pulley,  a  man  may  raise  himself  up  to 
the  mast  head  by  his  own  weight.    Suppose  a  rope  is  thrown 
over  a  pulley,  and  a  man  ties  one  end  of  it  round  his  body, 
and  takes  the  other  end  in  his  hands ;  he  may  raise  himself 
up,  because,  by  pulling  with  his  hands,  he  has  the  power 
of  throwing  more  of  his  weight  on  that  side  than  on  the 
other,  and  when  he  does  this  his  body  will  rise.     Thus,  al- 
though the  power  and  the  weight  are  the  same  individual, 
still  the  man  can  change  his  centre  of  gravity,  so  as  to  make 
the  power  greater  than  the  weight,  or  the  weight  greater 
than  the  power,  and  thus  can  elevate  one  half  his  weight  in 
succession. 

THE  INCLINED  PLANE. 

362.  The  fourth  simple   me-  Fig.  68. 
chanical   power  is   the   inclined 

plane. 

This  power  consists  of  a  plain, 
smooth  surface,  which  is  inclined 
towards,  or  from  the  earth.  It  is 
represented  by  fig.  68,  where 
from  a  to  b  is  the  inclined  plane ; 
the  line  from  d  to  a,  is  its  height, 
and  that  from  b  to  d,  its  base. 

In  compound  machines,  how  much  of  the  power  must  be  allowed  for 
the  friction  1  How  may  a  man  raise  himself  up  by  means  of  a  rope 
and  single  fixed  pulley  1  What  is  an  inclined  plane  1 


d 


86 


INCLINED  PLANE. 


A  board,  with  one  end  on  the  ground,  and  the  othe«  end 
resting  on  a  block,  becomes  an  inclined  plane. 

363.  This  machine,  being  both  useful  and  easily  con- 
structed, is  in  very  general  use,  especially  where  heavy 
bodies  are  to  be  raised  only  to  a  small  height.    Thus  a  man, 
by  means  of  an  inclined  plane,  which  he  can  readily  con- 
struct with  a  board,  or  couple  of  bars,  can  raise  a  load  into 
his  wagon,  which  ten  men  could  not  lift  with  their  hands. 

364.  The  power  required  to  force  a  given  weight  up  an 
inclined  plane,  is  in  a  certain  proportion  to  its  height,  and 
the  length  of  its  base,  or,  in  other  words,  the  force  must  be 
in  proportion  to  the  rapidity  of  its  inclination. 

365.  The  power  p,  Fig.  69. 
fig,  69,  pulling  a  weight 

up  the  inclined  plane, 
from  c  to  d,  only  raises 
it  in  a  perpendicular  di- 
rection from  e  to  d,  by 
acting  along  the  whole 
length  of  the  plane.  If 
the  plane  be  twice  as 
long  as  it  is  high,  that  is,  if  the  line  from  c  to  d  be  double 
the  length  of  that  from  e  to  d,  then  one  pound  at  p  will  bal- 
ance two  pounds  any  where  between  d  and  c.  It  is  evident, 
by  a  glance  at  this  figure,  that  were  the  base,  that  is,  the  line 
from  e  to  c,  lengthened,  the  height  from  e  to  d  being  the  same, 
that  a  less  power  at  p,  would  balance  an  equal  weight  any 
where  on  the  inclined  plane ;  and  so,  on  the  contrary,  were 
the  base  made  shorter,  that  is,  the  plane  more  steep,  the 
power  must  be  increased  in  proportion. 

366.  Suppose  two  inclined  Fig.  70. 
planes,  fig.  70,  of  the  same 

height,  with  bases  of  differ- 
ent lengths  ;  Ihen  the  weight 
and  power  will  be  to  each 
other  as  the  length  of  the 
planes.  If  the  length  from  a' 
a  to  b,  is  two  feet,  and  that 


On  what  occasions  is  this  power  chiefly  used  7  Suppose  a  man 
wants  to  load  a  barrel  of  cider  into  his  wagon,  how  does  he  make  an 
inclined  plane  for  this  purpose  1  To  roll  a  given  weight  up  an  inclined 
plane,  to  what  must  the  force  be  proportioned  1  Explain  fig.  G9.  If  the 
length  of  the  long  plane,  fig.  70,  be  double  that  of  the  short  one,  what 
must  be  the  proportion  between  the  power  and  the  weight  1 


INCLINED  PLANE.  87 

from  b  to  c,  one  foot,  then  two  pounds  at  d  will  balance  four 
pounds  at  w,  and  so  in  tnis  proportion,  whether  the  planes 
be  longer  or  shorter. 

367.  The  same  principle,  with  respect  to  the  vertical  ve- 
locities of  the  weight  and  powers,  applies  to  the  inclined 
plane,  in  common  with  the  other  mechanical  powers. 

Suppose   the   inclined    plane,  Fig.  71. 

fig.  7 1 ,  to  be  two  feet  from  a  to 
b,  and  one  foot  from  c  to  b,  then, 
as  we  have  already  seen  by  fig. 
69,  a  power  of  one  pound  at  p, 
would  balance  a  weight  of  two 
pounds  at  w.  Now,  in  the  fall 
of  the  power  to  draw  up  the 
weight,  it  is  obvious  that  its  ver- 
tical descent  must  be  just  twice 
the  vertical  ascent  of  the  weight ; 

for  the  power  must  fall  down  the  distance  from  a  to  b,  to 
draw  the  weight  that  distance ;  but  the  vertical  height  to 
which  the  weight  w  is  raised,  is  only  from  c  to  b.  Thus 
the  power,  being  two  pounds,  must  fall  two  feet,  to  raise  the 
weight,  four  pounds,  one  foot;  and  thus  the  power  and 
weight,  multiplied  by  the  several  velocities,  are  equal. 

368.  When  the  power  of  an  inclined  plane  is  considered 
as  a  machine,  it  must  therefore  be  estimated  by  the  proportion 
which  the  length  bears  to  the  height ;  the  power  being  in- 
creased in  proportion  as  the  elevation  of  the  plain  is  dimin- 
ished. 

Hilly  roads  maybe  regarded  as  inclined  planes,  and  loads 
drawn  upon  them  in  carriages,  considered  in  reference  to 
the  powers  which  impel  them,  and  subject  to  all  the  con- 
ditions which  we  have  stated,  with  respect  to  inclined  planes. 

369.  The  power  required  to  draw  a  load  up  a  hill,  is  in 
proportion  to  the  length  and  elevation  of  the  inclined  plane. 
On  a  road,  perfectly  horizontal,  if  the  power  is  sufficient  to 
overcome  the  friction,  and  the  resistance  of  the  atmosphere, 
the  carriage  will  move.     But  if  the  road  rise  one  foot  in 
fifteen,  besides  these  impediments,  the  moving  power  will 
have  to  lift  one  fifteenth  part  of  the  load. 

370.  If  two  roads  rise,  one  at  the  rate  of  a  foot  in  fifteen 
feet,  and  another  at  the  rate  of  a  foot  in  twenty,  then  the 

What  is  said  of  the  application  of  the  law  of  vertical  velocities  to 
the  inclined  plane?  Explain  fig.  71,  and  show  why  the  power  must 
fall  twice  as  far  as  the  weight  rises. 


88  THE  WEDGE, 

same  power  that  would  move  a  given  weight  fifteen  feet  on 
the  one,  would  move  it  twenty  feet  on  the  other,  in  the  same 
time. 

In  the  building  of  roads,  therefore,  both  speed  and  power 
are  very  often  sacrificed  to  want  of  judgment,  or  ignorance 
of  these  laws. 

371.  A  road,  as  every  traveller  knows,  is  often  continued 
directly  over  a  hill,  when  half  the  power,  with  the  increase 
of  speed,  on  a  level  road  around  it,  would  gain  the  same  dis- 
tance in  half  the  time.  v 

Besides,  where  is  there  a  section  of  country  in  which  the 
traveller  is  not  vexed  with  roads,  passing  straight  over  hills, 
when  precisely  the  same  distance  would  carry  him  around 
them  on  a  level  plane.  To  use  a  homely,  but  very  perti- 
nent illustration,  "  the  bale  of  a  pot  is  no  longer,  when  it 
lies  down,  than  when  it  stands  up."  Had  this  simple  fact 
been  noticed,  and  its  practical  bearing  carried  into  effect  by 
road  makers,  many  a  high  hill  would  have  been  shunned 
for  a  circuit  around  its  base,  and  many  a  poor  horse,  could  he 
speak,  would  thank  the  wisdom  of  such  an  invention. 

THE  WEDGE. 

372.  The  next  simple  mechanical  power  is  the  wedge. 
This  instrument  may  be  considered  as  two  inclined  planes, 
placed  base  to  base.     It  is  much  employed  for  the  purpose 
of  splitting  or  dividing  solid  bodies,  such  as  wood  and  stone, 

Fig.  72  represents  such  a  wedge  as  is  usually  Fig.  72. 
employed  in  cleaving  timber.  This  instrument 
is  also  used  in  raising  ships,  and  preparing  them 
to  launch,  and  for  a  variety  of  other  purposes. 
Nails,  awls,  needles,  and  many  cutting  instru- 
ments, act  on  the  principle  of  this  machine. 

There  is  much  difficulty  in  estimating  the 
power  of  the  wedge,  since  this  depends  on  the 
force,  or  the  number  of  blows  given  it,  together 
with  the  obliquity  of  its  sides.  A  wedge  of 
great  obliquity  would  require  hard  blows  to 
drive  it  forward,  for  the  same  reason  that  a  plane, 
much  inclined,  requires  much  force  to  roll  a 
heavy  body  up  it.  But  were  the  obliquity  of  the 
wedge,  and  the  force  of  each  blow  given,  still  it  would  be 

On  what  principle  does  the  wedge  act  1  In  what  case  is  this  power 
useful  1  What  common  instruments  act  on  the  principle  of  the  wedge  1 
What  difficulty  is  there  in  estimating  the  power  of  the  wedge  ? 


SCREW  89 

difficult  to  ascertain  the  exact  power  of  the  wedge  in  ordi- 
nary cases,  for,  in  the  splitting  of  timber  and  stone,  for  in- 
stance, the  divided  parts  act  as  levers,  and  thus  greatly  in- 
crease the  power  of  the  wedge.  Thus,  in  a  log  of  wood, 
six  feet  long,  when  split  one  half  of  its  length,  the  other  half 
is  divided  with  ease,  because  the  two  parts  act  as  levers,  the 
lengths  of  which  constantly  increase,  as  the  cleft  extends 
from  the  wedge. 

THE  SCREW. 

373.  The  screw  is  the  fifth  and  last  simple  mechanical 
power.     It  may  be  considered  as  a  modification  of  the  in- 
clined plane,  or  as  a  winding  wedge.      It  is  an  inclined 
plane    running   spirally  round  a  Fig.  73. 
spindle,  as  will  be  seen  by  fig.  73. 

Suppose  a  to  be  a  piece  of  paper, 
cut  into  the  form  of  an  inclined 
plane,  and  -rolled  round  the  piece 
of  wood  d ;  its  edge  would  form 
the  spiral  line,  called  the  thread 
of  the  screw. 

If  the  finger  be  placed  between 
the  two  threads  of  a  screw,  and  the  screw  be  turned  round 
once,  the  finger  will  be  raised  upward  equal  to  the  distance 
of  the  two  threads  apart.  In  this  manner,  the  finger  is 
raised  up  the  inclined  plane,  as  it  runs  round  the  cylinder 

374.  The  power  of  the  screw  is 
transmitted  and  employed  by  means 
of   another   screw   called   the   nut, 
through  which  it  passes.     This  has 
a  spiral  groove  running  through  it, 
which  exactly  fits  the  thread  of  the 
screw. 

375.  If  the  nut  is  fixed,  the  screw 
itself,  on  turning  it  round,  advances 
forward ;  but  if  the  screw  is  fixed, 
the    nut,   when    turned,    advances 
along  the  screw. 

Fig.  74  represents  the  first  kind       ^_ ^ 

of  screw,  being  such  as  is  commonly- 

used  in  pressing  paper,  and  other  substances.     The  nut,  n% 

On  what  principle  does  the  screw  act  1  How  is  it  shown  that  the 
screw  is  a  modification  of  the  inclined  plane  ?  Explain  fig.  74.  Which 
is  the  screw,  and  which  the  nut  1 

8* 


Fig.  74. 


90 


SCREW. 


through  which  the  screw  passes,  answers  also  for  one  of  the 
beams  of  the  press.  If  the  screw  be  turned  to  the  right,  il 
will  advance  downwards,  while  the  nut  stands  stih 

376.  A  screw  of  the   second 
kind   is  represented  by  fig.   75. 
In  this,  the  screw  is  fixed,  while 
the  nut,  n,  by  being  turned  by  the 
lever,  /,  from  right  to  left,  will 
advance  down  the  screw. 

377.  In.  practice,  the  screw  is 
never  used  as  a  simple  mechani- 
cal machine;  the  power  being  al- 
ways applied  by  means  of  a  lever, 
passing  through  the  head  of  the 
screw,  as  in  fig.  74,  or  into  the 
nut,  as  in  fig.  75. 

The  screw,  therefore,  acts  with 

the  combined  power  of  the  inclined  plane  and  the  lever,  and 
its  force  is  such  as  to  be  limited  only  by  the  strength  of  the 
materials  of  which  it  is  made. 

378.  In  investigating  the  effects  of  this  machine,  we  must, 
therefore,  take  into  account  both  these  simple  mechanical 
powers,  so  that  the  screw  now  becomes  really  a  compound 
engine. 

379.  In  the  inclined  plane,  we  have  already  seen,  that 
the  less  it  is  inclined,  the  more  easy  is  the  ascent  up  it.     In 
applying  the  same  principle  to  the  screw,  it  is  obvious,  that 
the  greater  the  distance  of  the  threads  from  each  other,  the 
more  rapid  the  inclination,  and,  consequently,  the  greater 
must  be  the  power  to  turn  it,  under  a  given  weight.    On  the 
contrary,  if  the  thread  inclines  downwards  but  slightly,  il 
will  turn  with  less  power,  for  the  same  reason  that  a  man 
can  roll   a  heavy  weight   up  a  plane  but  little  inclined. 
Therefore,  the  finer  the  screw,  or  the  nearer  the  threads  to 
each  other,  the  greater  will  be  the  pressure  under  a  given 
power. 

380.  Let    us  suppose  two  screws,  the  one  having  th« 

Which  way  must  the  screw  be  turned,  to  make  it  advance  througl 
the  nut  1  How  does  the  screw,  fig.  75,  differ  from  fig.  74  1  Is  the  screy 
ever  used  as  a  simple  machine  1  By  what  other  simple  power  is  i 
moved  1  What  two  simple  mechanical  powers  are  concerned  in  tb 
force  of  the  screw*?  Why  does  the  nearness  of  the  threads  make  a  dit 
ference  in  the  force  of  the  screw  1  Suppose  one  screw,  with  its  thread » 
one  inch  apart,  and  another  half  an  inch  apart,  what  will  be  their  dit* 
ference  in  force  1 


SCREW.  91 

threads  one  inch  apart,  and  the  other  half  an  inch  apart ; 
then  the  force  which  the  first  screw  will  give  with  the 
same  power  at  the  lever  will  be  only  half  that  given  by  the 
second.  The  second  screw  must  be  turned  twice  as  many 
times  round  as  the  first,  to  go  through  the  same  space,  but 
what  is  lost  in  velocity  is  gained  in  power.  At  the  lever  of 
the  firsV  two  men  would  raise  a  given  weight  to  a  given 
height  by  making  one  revolution  ;  while  at  the  lever  of  the 
second,  one  man  would  raise  the  same  weight  to  the  same 
height,  by  making  two  revolutions. 

381.  It  is  apparent  that  the  length  of  the  inclined  plane, 
up  which  a  body  moves  in  one  revolution,  is  the  circumfer- 
ence of  the  screw,  and  its  height,  the  interval  between  the 
threads.     The  proportion  of  its  power  would  therefore  be 
"  as  the  circumference  of  the  screw,  to  the  distance  between 
the  threads,  so  is  the  weight  to  the  power." 

382.  By  this  rule  the  power  of  the  screw  alone  can  be 
found ;  but  as  this  machine  is  moved  by  means  of  the  lever, 
we  must  estimate  its  force  by  the  combined  power  of  both. 
In  this  case,  the  circumference  described  by  the  end  of  the 
lever  employed,  is  taken,  instead  of  the  circumference  of  the 
screw  itself.     The  means  by  which  the  force  of  the  screw 
may  be  found,  is  therefore  by  multiplying  the  circumference 
which  the    lever  describes    by  the  power.       Thus,    "  the 
power  multiplied  by  the  circumference  which  it  describes,  is 
equal  to  the  weight  or  resistance,  multiplied  by  the  distance 
between  the  two  contiguous  threads}1      Hence  the  efficacy 
of  the  screw  maybe  increased,  by  increasing  the  length  of 
the  lever  by  which  it  is  turned,  or  by  diminishing  the  dis- 
tance between  the  threads.   If,  then,  we  know  the  length  of 
the  lever,  the  distance  between  the  threads,  and  the  weight 
to  be  raised,  we  can  readily  calculate  the  power ;   or,  the 
power  being  given,  and  the  distance  of  the  threads  and  the 
length  of  the  lever  known,  we   can  estimate  the  weight 
the  screw  will  raise. 

383.  Thus,  suppose  the  length  of  the  lever  to  be  forty 
inches,  the  distance  of  the  threads  one  inch,  and  the  weight 
8000  pounds ;  required,  the  power,  at  the  end  of  the  lever,  to 
raise  the  weight. 

What  is  the  length  of  the  inclined  plane  up  which  a  body  moves  by 
one  revolution  of  the  screw  1  What  would  be  the  height  to  which  the 
same  body  would  move  at  one  revolution  1  How  is  the  force  of  the 
screw  estimated  1  How  may  the  efficacy  of  the  screw  be  increased  1 
The  length  of  the  lever,  the  distance  between  the  threads,  and  the 
weight  being  known,  how  can  the  power  be  found  1 


92 


SCREW. 


384.  The  lever  being  40  inches,  the  diameter  of  the  cir- 
cle, which  the  end  describes,  is  80  inches.     The  circumrer- 
ence  is  a  little  more  than  three  times  the  diameter,  but  we 
will  call  it  just  three  times.     Then,  80X3=240  inches,  the 
circumference  of  the  circle.     The  distance  of  the  threads  is 
1  inch,  and  the  weight  8000  pounds.     To  find  the  power, 
multiply  the  weight  by  the  distance  of  the  threads,  and  di- 
vide by  the  circumference  of  the  circle.     Thus, 

circum.  in.  weight.  power. 

240        XI         :  :        8000        =         33i 
The  power  at  the  end  of  the  lever  must  therefore  be  33| 
pounds.     In  practice  this  power  would  require  to  be  in- 
creased about  one  third,  on  account  of  friction. 

385.  Perpetual  Screiv. — The  force  of  the  screw  is  some- 
times employed  to  turn  a  wheel,  by  acting  on  its  teeth.     In 
this  case  it  is  called  the  perpetual  screw. 

386.  Fig.  76  represents  such  Fig.  76. 
a  machine.     It  is  apparent,  that 

by  turning  the  crank  c,  the  wheel 
will  revolve,  for  the  thread  of  the 
screw  passes  between  the  cogs 
of  the  wheel.  By  means  of  an 
axle,  through  the  centre  of  this 
wheel,  like  the  common  wheel 
and  axle,  this  becomes  an  ex- 
ceedingly powerful  machine,  but 
like  all  other  contrivances  for  ob- 
taining great  power,  its  effective 
motion  is  exceedingly  slow.  It 
has,  however,  some  disadvantages,  and  particularly  the  great 
friction  between  the  thread  of  the  screw  and  the  teeth  of  the 
wheel,  which  prevents  it  from  being  generally  employed  to 
raise  weights. 

387.  All  these  Mechanical  Powers  resolved  into  three. — 
We  have  now  enumerated  and  described  all  the  mechanical 
powers  usually  denominated  simple.  They  are  five  in  num- 
ber, namely,  the  Lever,  Wheel  and  Axle,  Pulley,  Wedge, 
Inclined  Plane,  and  Screw. 

388.  In  respect  to  the  principle  on  which  they  act,  they 
may  be  resolved  into  three  simple  powers,  namely,  the  lever, 
the  inclined  plane,  and  the  pulley;  for  it  has  been  shown 

Give  an  example.  What  is  the  screw  called  when  it  is  employed 
to  turn  a  wheel"?  What  is  the  object  of  this  machine  for  raising 
weights  1  How  many  simple  mechanical  powers  are  there  1  and  what 
are  they  called?  How  can  they  be  resolved  into  three  simple  powers  1 


SCREW.  93 

that  the  wheel  and  axle  is  only  another  form  of  the  lever, 
and  that  the  screw  is  but  a  modification  of  the  inclined  plane. 

389.  It  is  surprising,  indeed,  that  these,  simple  powers 
can  be  so  arranged  and  modified,  as  to  produce  the  different 
actions  in  all  that  vast  variety  of  intricate  machinery  which 
men  have  invented  and  constructed. 

390.  The  variety  of  motions  we  witness  in  the  little  en- 
gine which  makes  cards,  by  being  supplied  with  wire  for 
the  teeth,  and  strips  of  leather  to  stick  them  through,  would 
itself  seem  to  involve  more  mechanical  powers  than  those 
enumerated.     This  engine  takes  the  wire  from  a  reel, bends 
it  into  the  form  of  teeth  ;  cuts  it  off;  makes  two  holes  in  the 
leather  for  the  tooth  to  pass  through ;    sticks  it  through ; 
then  gives  it  another  bend,  on  the  opposite  side  of  the  leather ; 
graduates  the  spaces  between  the  rows  of  teeth,  and  between 
one  tooth  and  another ;  and,  at  the  same  time,  carries  the 
leather  backwards  and  forwards,  before  the  point  where  the 
teeth  are  introduced,  with  a  motion  so  exactly  correspond- 
ing with  the  motions  of  the  parts  which  make  and  stick  the 
teeth,  as  not  to  produce  the  difference  of  a  hair's  breadth  in 
the  distance  between  them. 

391.  All  this  is  done  without  the  aid  of  human  hands, 
any  farther  than  to  put  the  leather  in  its  place,  and  turn  a 
crank ;  or,  in  some  instances,  many  of  these  machines  are 
turned  at  once,  by  means  of  three  or  four  dogs,  walking  on 
an  inclined  plane  which  revolves. 

392.  Such  a  machine  displays  the  wonderful  ingenuity 
and  perseverance  of  man,  and  at  first  sight  would  seem  to 
set  at  nought  the  idea  that  the  lever  and  wh^el  were  the 
chief  simple  powers  concerned  in  its  motions.     But  when 
these  motions  are  examined  singly  and  deliberately,  we  are 
soon  convinced  that  the  wheel,  variously  modified,  is  the 
principal  mechanical  power  in  the  whole  engine. 

393.  Use  of  Machinery. — It  has  already  been  stated,  (332) 
that  notwithstanding  the  vast  deal  of  time  and  ingenuity 
which  men  have  spent  on  the  construction  of  machinery, 
and  in  attempting  to  multiply  their  powers,  there  has,  as 
yet,  been  none  produced,  in  which  the  power  was  not  ob- 
tained at  the  expense  of  velocity,  or  velocity  at  the  expense 
of  power ;  and,  therefore,  no  actual  force  is  ever  generated 
fey  machinery. 

What  is  said  of  the  card  making  machine  1  What  are  the  chief 
mechanical  powers  concerned  in  its  motions  1  Is  there  any  actual  foice 
generated  by  machinery  7  Can  great  velocity  and  great  force  be  pro- 
d  uced  by  the  same  machinery  1  W  hy  not  1 


94 


HYDROSTATICS. 


394.  Suppose  a  man  able  to  raise  a  weight  by  means  of  a 
compound  pulley  of  ten  ropes,  which  it  would  take  ten  men 
to  raise,  by  one  rope,  without  pulleys.      If  the  weight  is 
to  be  raised  a  yard,  the  ten  men  by  pulling  their  rope  a  yard 
will  do  the  work.     But  the  man  with  the  pulleys  must  draw 
his  rope  ten  yards  to  raise  the  weight  one  yard,  and  in  ad- 
dition to  this,  he  has  to  overcome  the  friction  of  the  ten  pul- 
leys, making  about  one  third   more  actual  labour  than  was 
employed  by  the  ten  men.     But  notwithstanding  these  in- 
conveniences, the  use  of  machinery  is  of  vast  importance  to 
the  world. 

395.  On  board  of  a  ship,  a  few  men  will  raise  an  anchor 
with  a  capstan,  which  it  would  take  ten  or  twenty  times  the 
same  number  to  raise  without  it,  and  thus  the  expense  of 
shipping  men  expressly  for  this  purpose  is  saved. 

396.  One  man  with  a  lever,  may  move  a  stone  which  it 
would  take  twenty  men  to  move  without  it,  and  though  it 
should  take  him  twenty  times  as  long,  he  would  still  be  the 
gainer,  since  it  would  be  more  convenient,  and  less  expen- 
sive for  him  to  do  the  work  himself,  than  to  employ  twenty 
others  to  do  it  for  him. 

397.  When  men  employ  the  natural  elements  as  a  power 
to  overcome  resistance  by  means  of  machinery,  there  is  a 
vast  saving  of  animal  labour.     Thus  mills,  and"  all  kinds  of 
engines,  which  are  kept  in  motion  by  the  power  of  water,  or 
wind,  or  steam,  save  animal  labour  equal  to  the  power  it 
takes  to  keep  them  in  motion. 

HYDROSTATICS. 

398.  Hydrostatics   is  the  science   which   treats   of  the 
weight,  pressure,  and  equilibrium  of  water,  or  other  fluids, 
when  in  a  state  of  rest. 

399.  Hydraulics  is  that  part  of  the  science  of  fluids  which 
treats  of  water  in  motion,  and  the  means  of  raising  and 
conducting  it  in  pipes,  or  otherwise,  for  all  sorts  of  purposes. 

400.  The  subject  of  water  at  rest,  will  first  claim  investi- 
gation, since  the  laws  which  regulate  its  motion  will  be  best 
understood  by  first  comprehending  those  which  regulate  its 
pressure. 

401.  A  fluid  is  a  substance  whose  particles  are  easily 
moved  among  each  other,  as  air  and  water. 

Which  performs  the  greatest  labour,  ten  men  who  lift  a  weight  with 
their  hands,  or  one  man  who  does  the  same  with  ten  pulleys  7  Why  1 
What  is  hydrostatics  1  How  does  hydraulics  differ  from  hydrostatics  1 
What  is  a  fluid  1 


HYDROSTATICS.  95 

402.  The  air  is  called  an  elastic  fluid,  because  it  iseasily 
compressed  into  a  smaller  bulk,  and  returns  again  to  its  ori- 
ginal state  when  the  pressure  is  removed.     Water  is  called 
a  mw-elastic  fluid,  because  it  admits  of  little  diminution  of 
bulk  under  pressure. 

403.  The  non-elastic  fluids,  are  perhaps  more  properly 
called  liquids,  but  both  terms  are  employed  to  signify  water 
and  other  bodies  possessing  its  mechanical  properties.    The 
term  fluid,  when  applied  to  the  air,  has  the  word  elastic  be- 
fore it. 

404.  One  of  the  most  obvious  properties  of  fluids,  is  the 
facility  with  which  they  yield  to  the  impressions  of  other 
bodies,  and  the  rapidity  with  which  they  recover  their  form- 
er state,  when  the  pressure  is  removed.     The  cause  of  this, 
is  apparently  the  freedom  with  which  the  particles  of  liquids 
slide  over,  or  among  each  other;  their  cohesive  attraction 
being  so  slight  as  to  be  overcome  by  the  least  impression. 
On  this  want  of  cohesion  among  their  particles  seem  to  de- 
pend the  peculiar  mechanical  properties  of  these  bodies. 

405.  In  solids,  there  is  such  a  connexion  between  the 
particles,  that  if  one  part  moves,  the  other  part  must  move 
also.     But  in  fluids,  one  portion  of  the  mass  may  be  in  mo- 
tion, while  the  other  is  at  rest.     In  solids,  the  pressure  is 
always  downwards,  or  towards  the  centre  of  the  earth's 
gravity  ;  but  in  fluids  the  particles  seem  to  act  on  each  other 
as  wedges,  and  hence,  when  confined,  the  pressure  is  side- 
ways, and  even  upwards,  as  well  as  downwards. 

406.  Water  has  commonly  been  called  a  non-Fig.^77. 
elastic  substance,  but  it  is  found  that  under  great 
pressure  its  volume  is  diminished,  and  hence  it  is 
proved  to  be  elastic.     The  most  decisive  experi- 
nents  on  this  subject  were  made  within  a  few  years 

by  Mr.  Perkins. 

407.  The  experiments  were  made  by  means  of  a 
hollow  cylinder,  fig.  77,  which  was  closed  at  the 
bottom,  and  made  water  tight  at  the  top,  by  a  cap, 
screwed  on.      Through  this  cap,  at  a,  passed  the 
rod  b,  which  was  five  sixteenths  of  an  inch  in  diam- 
eter. The  rod  was  so  nicely  fitted  to  the  cap,  as  also 
to  be  water  tight      Around  the  rod  at  c,  there  was 
placed  a  flexible  ring,  which  could  be  easily  push- 

•    What  is  an  elastic  fluid  1    Why  is  air  called  an  elastic  fluid  ?  What 
substances  are  called  liquids  1     What  is  one  of  the  most  obvious  pro- 
}uids  1    On  what  do  the  peculiar  mechanical  properties  of 


perties  of  liqu 
fluids  depend 


»0  HYDROSTATICS. 

ed  up  or  down,  but  fitted  so  closely  as  to  remain  on  any 
part  where  it  was  placed. 

408.  A  cannon  of  sufficient  size  to  receive  this  cylinder, 
which  was  three  inches  in  diameter,  was  furnished  with  a 
strong  cap  and  forcing  pump,  and  set  vertically  into  the 
ground.     The  cannon  and  cylinder  were  next  filled  with 
water,  and  the  cylinder,  with  its  rod  drawn  out,  and  the  ring 
placed  down  to  the  cap,  as  in  the  figure,  was  plunged  into 
the  cannon.     The  water  in  the  cannon  was  then  subjected 
to  an  immense  pressure  by  means  of  the  forcing  pump,  af- 
ter which,  on  examination  of  the  apparatus,  it  was  found 
that  the  ring  c,  instead  of  being  where  it  was  placed,  was 
eight  inches  up  the  rod.      The  water  in  the  cylinder  being 
compressed  into  a  smaller  space,  by  the  pressure  of  that  in 
the  cannon,  the  rod  was  driven  in,  while  under  pressure, 
but  was  forced  out  again  by  the  expansion  of  the  water, 
when  the  pressure  was  removed.     Thus,  the  ring  on  the 
rod  would  indicate  the  distance  to  which  it  had  been  forced 
in,  during  the  greatest  pressure. 

409.  This   experiment   proved    that   water,    under   the 
pressure  of  one  thousand  atmospheres,  that  is,  the  weight  of 
15,000  pounds  to  the  square  inch,  was  reduced  in  bulk  about 
one  part  in  24. 

410.  So  slight  a  degree  of  elasticity  under  such  immense 
pressure,  is  not  appreciable  under  ordinary  circumstances, 
and  therefore  in  practice,  or  in  common  experiments  on  this 
fluid,  water  is  considered  as  non-elastic. 

EQUAL  PRESSURE  OF  WATER. 

411.  The  particles  of  water,  and  other  fluids,  when  con- 
fined, press  on  the  vessel  which  confines  them,  in  all  direc- 
tions, both  upwards,  downwards,  and  sideways. 

From  this  property  of  fluids,  together  with  their  weight, 
or  gravity,  very  unexpected  and  surprising  effects  are  pro- 
duced. 

412.  The  effect  of  this  property,  which  we  shall  first  ex- 
amine, is,  that  a  quantity  of  water,  however  small,  will, 
balance  another  quantity  however  large.     Such  a  proposi- 

In  what  respect  does  the  pressure  of  a  fluid  differ  from  that  of  a  sond  1 
Is  water  an  elastic,  or  non-elastic  fluid  1  Describe  fig.  77,  and  show- 
now  water  was  found  to  be  elastic?  In  what  proportion  does  the  bulk 
of  water  diminish  under  a  pressure  of  15,000  pounds  to  the  square, 
inch  1  In  common  experiments,  is  water  considered  elastic,  or  nort 
elastic  1  When  water  is  confined,  in  what  direction  does  it  press  1 


HYDROSTATICS. 


97 


Fig.  78. 


tion  at  first  thought  might  seem  very  improbable.  But  on 
examination,  we  shall  find  that  an  experiment  with  a  very 
simple  apparatus  will  convince  any  one  of  its  truth.  In- 
deed, we  every  day  see  this  principle  established  by  actual 
experiment,  as  will  be  seen  directly. 

413.  Fig.  78  represents  a  common  cof- 
fee-pot, supposed  to  be  filled  up  to  the  dot- 
ted line  a,  with  a  decoction  of  coffee,  or 
any  other  liquid.     The  coffee,  we  know, 
stands  exactly  at  the  same  height,  both  in 
the   body  of  the   pot,  and  in  its  spout. 
Therefore,  the  small  quantity  in  the  spout, 
balances  the  large  quantity  in  the  pot,  or 

presses  with  the  same  force  downwards,  as  that  in  the  body 
of  the  pot  presses  upwards.  This  is  obviously  true,  other- 
wise, the  large  quantity  would  sink  below  the  dotted  line, 
while  that  in  the  spout  would  rise  above  it,  and  run  over. 

414.  The  same  principle  is  more  strik-  Fig.  79. 
ingly  illustrated  by  fig.  79.  c 

Suppose  the  cistern  a  to  be  capable  of 
holding  one  hundred  gallons,  and  into  its 
bottom  there  be  fitted  the  tube  b,  bent,  as 
seen  in  the  figure,  and  capable  of  con- 
taining one  gallon.  The  top  of  the  cis- 
tern, and  that  of  the  tube,  being  open, 
pour  water  into  the  tube  at  c,  and  it  will 
rise  up  through  the  perpendicular  bend 
into  the  cistern,  and  if  the  process  be  con- 
tinued, the  cistern  will  be  filled  by  pour- 
ing water  into  the  tube.  Now,  it  is  plain,  that  the  gallon 
of  water  in  the  tube,  presses  against  the  hundred  gallons  in 
the  cistern,  with  a  force  equal  to  the  pressure  of  the  hun- 
dred gallons,  otherwise,  that  in  the  tube  would  be  forced  up- 
wards higher  than  that  in  the  cistern,  whereas,  we  find  that 
the  surfaces  of  both  stand  exactly  at  the  same  height. 

415.  From  these  experiments  we  learn,  "  that  the  press- 
ure of  a  fluid  is  not  in  proportion  to  its  quantity,  but  to  its 
height,  and  that  a  large  quantity  of  water  in  an  open  ves- 
sel, presses  down  with  no  more  force,  than  a  small  quantity 
of  the  same  height." 

How  does  the  experiment  with  the  coffee-pot  show  that  a  small  quan- 
tity of  liquid  will  balance  a  large  one  1  Explain  fig.  79,  and  show  how 
the  pressure  in  the  tube  is  equal  to  the  pressure  in  the  cistern.     What 
conclusion,  or  general  truth,  is  to  be  drawn  from  these  experimental 
0 


HYDROSTATICS. 

416.  In  this  respect,  the  size  or  shape  of  a  vessel  is  of  no 
consequence,  for  if  a  number  of  vessels,  differing  entirely 
from  each  other  in  figure,  position,  and  capacity,  have  a 
communication  made  between  them,  and  one  be  filled  with 
water,  the  surface  of  the  fluid,  in  all,  will  be  at  exactly  the 
same  elevation.  If,  therefore,  the  water  stands  at  an  equal, 
height  in  all,  the  pressure  in  one  must  be  just  equal  to  that 
in  another,  and  so  equal  to  that  in  all  the  others. 
Fig.  80. 


417.  To  make  this  obvious,  suppose  a  number  of  vessels, 
of  different  shapes  and  sizes,  as  represented  by  fig.  80,  to 
have  a  communication  between  them,  by  means  of  a  small 
tube,  passing  from  the  one  to  the  other.     If,  now,  one  of 
these  vessels  be  filled  with  water,  or  if  water  be  poured  into 
the  tube  a,  all  the  other  vessels  will  be  filled  at  the  same  in- 
stant, up  to  the  line  b  c.     Therefore,  the  pressure  of  the 
water  in  a,  balances  that  in  1,  2,  3,  &c.,  while  the  pressure 
in  each  of  these  vessels,  is  equal  to  that  in  the  other,  and  so 
an  equilibrium  is  produced  throughout  the  whole  series. 

418.  If  an  ounce  of  water  be  poured  into  the  tube  a,  it 
will  produce  a  pressure  on  the  contents  of  all  the  other  ves- 
sels, equal  to  the  pressure  of  all  the  others  on  the  tube  ;  for, 
it  will  force  the  water  in  all  the  other  vessels  to  rise  up- 
wards to  an  equal  height  with  that  in  the  tube  itself.    Hence, 
we  must  conclude,  that  the  pressure  in  each  vessel,  is  not 
only  equal  to  that  in  any  of  the  others,  but  also  that  the 
pressure  in  any  one,  is  equal  to  that  in  all  the  others. 

419.  From  this  we  learn,  that  the  shape  or  size  of  a  ves- 

What  difference  does  the  shape  or  size  of  a  vessel  make  in  respect 
to  the  pressure  of  a  fluid  on  its  bottom  ?  Explain  fig.  80,  and  show 
how  the  equilibrium  is  produced.  Suppose  an  ounce  of  water  be  pour- 
ed into  the  tube  a,  what  will  be  its  effect  on  the  contents  of  the  other 
vessels  1  What  conclusion  is  to  be  drawn  from  pouring  the  ounce  of 
water  into  the  tube  a  1 


H  S-DROSTATICS. 


99 


sel  has  no  influence  on  the  pressure  of  its  liquid  contents, 
but  that  the  pressure  of  water  is  as  its  height,  whether  the 
quantity  be  great  or  small.  We  learn,  also,  that  in  no  case 
will  the  weight  of  a  quantity  of  liquid,  however  large,  force 
another  quantity,  however  small,  above  the  level  of  its  own 
surface. 

420.  This  is  proved  by  experiment ;  for  if,  from  a  pond 
situated  on  a  mountain,  water  be  conveyed  in  an  inch  tube 
to  the  valley,  a  hundred  feet  below,  the  water  will  rise  just 
a  hundred  feet  in  the  tube  ;  that  is,  exactly  to  the  level  of 
the  surface  of  the  pond.     Thus  the  water  in  the  pond,  and 
that  in  the  tube,  press  equally  against  each  other,  and  pro- 
duce an  exact  equilibrium. 

Thus  far  we  have  considered  the  fluid  as  acting  only  in 
vessels  with  open  mouths,  and  therefore  at  liberty  to  seek 
its  balance,  or  equilibrium,  by  its  own  gravity.  Its  press- 
ure, we  have  seen,  is  in  proportion  to  its  height,  and  not  to 
its  bulk. 

421.  Now,  by  other  experiments,  it  is  ascertained,  that 
the  pressure  of  a  liquid  is  in  proportion  to  its  height,  and 
its  area  at  the  base. 

Suppose  a  vessel,  ten  feet  high,  and  Fig.  81. 

two  feet  in  diameter,  such  as  is  rep- 
resented at  #,  fig.  81,  to  be  filled 
with  water  ;  there  would  be  a  certain 
amount  of  pressure,  say  at  c,  near 
the  bottom.  Let  d  represent  another 
vessel,  of  the  same  diameter  at  the 
bottom,  but  only  a  foot  high,  and 
closed  at  the  top.  Now  if  a  small 
tube,  say  the  fourth  of  an  inch  in  di- 
ameter, be  inserted  into  the  cover  of 
the  vessel  d,  and  this  tube  be  carried 
to  the  height  of  the  vessel  a,  and 
then  the  vessel  and  tube  be  filled  \ 
with  water,  the  pressure  on  the  bot- 
toms and  sides  of  both  vessels  to  the  same  height  will  be 
equal,  and  jets  of  water  starting  from  d  and  c,  will  have  ex- 
actly the  same  force. 

What  is  the  reason  that  a  large  quantity  of  water  will  not  force  a 
small  quantity  above  its  own  level'?  Is  the  force  of  water  in  propor- 
tion to  its  height,  or  its  quantity  7  How  is  a  small  quantity  of  water 
shown  to  press  equal  to  a  large  quantity  by  fig.  81 7  Explain  the  reason 
why  the  pressure  is  as  great  at  d,  as  at  c. 


100  HYDROSTATICS. 

422.  This  might  at  first  seem  improbable,  but  to  convince 
ourselves  of  its  truth,  we  have  only  to  consider,  that  any  im- 
pression made  on  one  portion  of  the  confined  fluid  in  the 
vessel  d,  is   instantly  communicated   to   the  whole  mass. 
Therefore,  the  water  in  the  tube  b  presses  with  the  same 
force  on  every  other  portion  of  the  water  in  d,  as  it  does  on 
that  small  portion  over  which  it  stands. 

423.  This  principle  is  illustrated  in  a  very  striking  man- 
ner, by  the  experiment,  which  has  often  been  made,  of  burst- 
ing the  strongest  wine-cask  with  a  few  ounces  of  water. 

424.  Suppose  a,  fig.  82,  to  be  a  strong  cask,      Fig.  82. 
already  filled  with  water,  and  suppose  the  tube 

b,  thirty  feet  high,  to  be  screwed,  water  tight, 
into  its  head.  When  water  is  poured  into  the 
tube,  so  as  to  fill  it  gradually,  the  cask  will 
show  increasing  signs  of  pressure,  by  emitting 
the  water  through  the  pores  of  the  wood,  and 
between  the  joints ;  and,  finally,  as  the  tube  is 
filled,  the  cask  will  burst  asunder. 

425.  The  same  apparatus  will  serve  to  il- 
lustrate the  upward  pressure  of  water ;  for  if 
a  small  stop-cock  be  fitted  to  the  upper  head, 
on  turning  this,  when  the  tube  is  filled,  a  jet 
of  water  will  spirt  up  with  a  force,  and  to  a 
height,  that  will  astonish  all  who  never  before 
saw  such  an  experiment. 

In  theory,  the  water  will  spout  to  the  same 
height  with  that  which  gives  the  pressure,  but,  in  practice, 
it  is  found  to  fall  short,  in  the  following  proportions  : 

426.  If  the  tube  be  twenty  feet  high,  and  the  orifice  for 
the  jet  half  an  inch  in  diameter,  the  water  will  spout  nearly 
nineteen  feet.     If  the  tube  be  fifty  feet  high,  the  jet  will  rise 
upwards  of  forty  feet,  and  if  a  hundred  feet,  it  will  rise 
above  eighty  feet.     It  is  understood,  in  every  case,  that  the 
tubes  are  to  be  kept  full  of  water. 

The  height  of  these  jets  show  the  astonishing  effects  that 
a  small  quantity  of  fluid  produces  when,  pressing  from  a 
perpendicular  elevation. 

427.  Hydrostatic  Bellows. — An  instrument  called  the  hy- 

How  is  the  same  principle  illustrated  by  fig.  827  How  is  the  up- 
ward pressure  of  water  illustrated  by  the  same  apparatus  1  Under  the 
pressure  of  a  column  of  water  twenty  feet  high,  what  will  be  tH  height 
of  the  jet  7  Under  a  pressure  of  a  hundred  feet,  how  high  wilt  it  rise  1 
What  is  the  hydrostatic  bellows  ? 


HYDROSTATICS. 


101 


Fig.  83. 


drostatic  bellows,  a.so  shows,  in  a  striking  manner,  the  great 
force  of  a  small  quantity  of  water,  pressing  in  a  perpendic- 
ular direction. 

428.  This  instrument  consists  of  two  boards,  connected 
together  with  strong  leather,  in  the  manner  of  the  common 
bellows.     It  is  then  furnished  with  a 

tube  a,  fig.  83,  which  communicates 
between  the  two  boards.  A  person 
standing  on  the  upper  board,  may 
raise  himself  up  by  pouring  water  into 
the  tube.  If  the  tube  holds  an  ounce 
of  water,  and  has  an  area  equal  to  a 
thousandth  part  of  the  area  of  the  top 
of  the  bellows,  one  ounce  of  water  in 
the  tube  will  balance  a  thousand 
ounces  placed  on  the  bellows. 

429.  Hydraulic  Press. — This  prop- 
erty of  water  was  applied  by  Mr.  Bra- 
mah  to  the   construction   of  his  hy- 
draulic press.    But  instead  of  a  high 

tube  of  water,  which  in  most  cases  could  not  be  so  readily  ob- 
tained, he  substituted  a  strong  forcing  pump,  and  instead  of 
the  leather  bellows,  a  metallic  pump  barrel  and  piston. 

430.  This  arrangement  will  Fig.  84. 
be  understood  by  fig.  84,  where 

the  pump  barrel,  a,  b,  is  rep- 
resented as  divided  lengthwise,  r 
in  order  to  show  the  inside., 
The  piston,  c,  is  fitted  so  ac- 
curately to  the  barrel,  as  to 
work  up  and  down  water 
tight ;  both  barrel  and  piston 
being  made  of  iron.  The  thing 
to  be  broken,  or  pressed,  is 
laid  on  the  flat  surface,  i,  there  being  above  this,  a  strong 
frame  to  meet  the  pressure,  not  shown  in  the  figure.  The 
small  forcing  pump,  of  which  d  is  the  piston,  and  h,  the 
lever  by  which  it  is  worked,  is  also  made  of  iron. 

431.  Now,  suppose  the  space  between  the  small  piston 
and  the  large  one,  at  w,  to  be  filled  with  water,  then,  on 

What  property  of  water  is  this  instrument  designed  to  show  1   Ex- 
plain fi?.  84.  Where  is  the  piston  1  Which  is  the  pump  barrel,  in  wnlc*  ^ 
works  I  In  the  hydrostatic  press,  what  is  the  proportion  between  the  press- 
ure given  bv  the  small  piston,  and  the  force  exerted  on  the  large  one  1 
9* 


,02 


HYDROSTATICS. 


forcing  down  the  small  piston,  d,  there  will  be  a  pressure 
against  the  large  piston,  c,  the  whole  force  of  which  will 
be  in  proportion  as  the  aperture  in  which  c  works,  is  great- 
er than  that  in  which  d  works.  If  the  piston,  d,  is  half  an 
inch  in  diameter,  and  the  piston,  c,  one  foot  in  diameter, 
then  the  pressure  on  c  will  be  576  times  greater  than  that 
on  d.  Therefore,  if  we  suppose  the  pressure  of  the  small 
piston  to  be  one  ton,  the  large  piston  will  be  forced  up 
against  any  resistance,  with  a  pressure  equal  to  the  weight 
of  576  tons.  It  would  be  easy 'for  a  single  man  to  give  the 
pressure  of  a  ton  at  d,  by  means  of  the  lever,  and,  therefore, 
a  man,  with  this  engine,  would  be  able  to  exert  a  force  equal 
to  the  weight  of  near  600  tons. 

432.  It  is  evident,  that  the  force  to  be  obtained  by  this 
principle,  can  only  be  limited  by  the  strength  of  the  mate- 
rials of  which  the  engine  is  made.     Thus,  if  a  pressure  of 
two  tons  be  given  to  a  piston,  the  diameter  of  which  is  only 
a  quarter  of  an  inch,  the  force  transmitted  to  the  other  pis- 
ton, if  three  feet  in  diameter,  would  be  upwards  of  40,000 
tons ;  but  such  a  force  is  much  too  great  for  the  strength  of 
any  material  with  which  we  are  acquainted. 

433.  A  small  quantity  of  water,  extending  to  a  great  ele- 
vation, would  give  the  pressure  above  described,  it  being 
only  for  the  sake  of  convenience,  that  the  forcing  pump  is 
employed,  instead  of  a  column  of  water. 

434.  There  is  no  doubt,  but  in  the  operations  of  nature, 
great  effects  are  sometimes  produced  among  mountains,  by 
a  small  quantity  of  water  finding  its  way  to  a  reservoir  in 
the  crevices  of  the  rocks  far  beneath. 

435.  Sup-  Fig.  85. 
pose     in    the 

interior  of  a 
mountain,  fig. 
85,  there 

should  be  a 
ypace  of  ten 
yards  square, 
and  an  inch 
deep,  filled 
with  water, 
and  closed  up 

What  is  the  estimated  force  which  a  man  could  give  by  one  of  these 
engines  1  If  the  pressure  of  two  tons  be  made  on  a  piston  of  a  quar- 
ter of  an  inch  in  diameter,  what  will  be  the  force  transmitted  to  the 
other  piston  of  three  feet  in  diameter1? 


HYDROSTATICS.  103 

on  ail  sides ;  and  suppose,  that  in  the  course  of  time,  a  small 
fissure,  no  more  than  an  inch  in  diameter,  should  be  opened 
by  the  water,  from  the  height  of  two  hundred  feet  above, 
down  to  this  little  reservoir.  The  consequence  might  be, 
that  the  side  of  the  mountain  would  burst  asunder,  for  the 
pressure,  under  the  circumstances  supposed,  would  be  equal 
to  the  weight  of  five  thousand  tons. 

436.  Pressure  on  vessels  ivith  oblique  sides. — It  is  obvi- 
ous that  in  a  vessel,  the  sides  of  which  are  every  where  per- 
pendicular to  each  other,  that  the  pressure  on  the  bottom  will 
be  as  the  height,  and  that  the  pressure  on  the  sides  will 
every  where  be  equal  at  an  equal  depth  of  the  liquid. 

437.  But  it  is  not  so  obvious,  that  in  a  vessel   having 
oblique  sides,  that  is,  diverging  outwards  from  the  bottom, 
or  converging  from  the  bottom  towards  the  top,  in  what 
manner  the  force  of  pressure  will  be  sustained. 

438.  Now,  the  pressure  on  the  bottom  of  any  vessel,  no 
matter  what  the  shape  may  be,  is  equal  to  the  height  of  the 
fluid,  and  the  area  of  the  bottom. 

439.  Hence  the  pressure  > Fig.  86. ^ 

on  the  bottom  of  the  vessel "~ 

sloping  outwards,  fig.  86. 

will  be  just  equal  to  what 

it  would  be,  were  the  sides 

perpendicular,      and      the 

same  would  be  .the  case  did  the  sides  slope  inwards  instead 

of  outwards. 

440.  In  a  vessel  of  this  shape,  the  sides  sustain  a  pressure 
equal  to  the  perpendicular  height  of  the  fluid  above  any 
given  point.     Thus,  if  the  point  1  sustain  a  pressure  of  one 
pound,  2,  being  twice  as  far  below  the  surface,  will  have  a 
pressure  equal  to  two  pounds,  and  so  in  this  proportion  with 
respect  to  the  other  eight  parts  marked  on  the  side  of  the  vessel. 

441.  On  the  contrary,  did  the  sides  of  the  vessel  slope  in- 
wards instead  of  outwards,  as  re- 

presented  by  fig.  87,  still  the  same 
consequences  would  ensue,  that  is, 
the  perpendicular  height,  in  both 
cases,  would  make  -the  pressure 
equal.  For  although,  in  the  lat- 10:|| 
ter  case,  the  perpendicular  height 

What  is  the  pressure  of  water  in  the  crevices  of  mountains,  and  the 
consequences  1  What  is  the  pressure  on  the  bottom  of  a  vessel  contain- 
ing a  fluid  equal  to"?  Suppose  the  sides  of  the  vessel  slope  outwards, 
what  effect  does  this  produce  on  the  pressure  1 


104  WATER  LEVEL. 

is  not  above  the  point  pressed  upon,  still  the  same  effect  is 
produced  by  the  pressure  of  the  fluid  in  the  direction  per- 
pendicular to  the  plane  of  the  side,  and  since  fluids  press 
equally  hi  all  directions,  this  pressure  is  just  the  same  as 
though  it  were  perpendicularly  above  the  point  pressed 
upon,  as  in  the  direction  of  the  dotted  lines. 

442.  To  show  that  this  is  the  case,  we  will  suppose  that 
P,  fig.  87,  is  a  particle  of  the  liquid  at  the  same  depth  below 
the  surface  as  the  division  marked  5  on  the  side  of  the  ves- 
sel; this  particle  is  evidently  pressed  downwards  by  the  in- 
cumbent weight  of  the  column  of  fluid  P,  a.     But  since 
fluids  press  equally  in  all  directions,  this  particle  must  be 
pressed  upwards  and  sideways  with  the  same  force  that  it  is 
pressed  downwards,  and,  therefore,  must  be  pressed  from 
P  towards  the  side  of  the  vessel,  marked  5,  with  the  same 
force  that  it  would  be  if  the  pressure  was  perpendicular 
above  that  part  of  the  vessel. 

443.  From  all  that  has  been  stated,  we  learn,  that  if  the 
sides  of  the  vessels,  86  and  87,  be  equally  inclined,  though 
in  contrary  directions  to  their  bottoms,  and  the  vessels  be 
filled  with  equal  depths  of  water,  the  sides  being  of  equal  di- 
mensions, will  be  pressed  equally,  though  the  actual  quan 
tity  of  fluid  in  each,  be  quite  different  from  each  other. 

WATER  LEVEL. 

444.  We  have  seen,  that  in  whatever  situation  water  is 
placed,  it  always  tends  to  seek  a  level.     Thus,  if  several  ves- 
sels communicating  with  each  other  be  filled  with  water, 
the  fluid  will  be  at  the  same  height  in  all,  and  the  level  will 
be  indicated  by  a  straight  line  drawn  through  all  the  ves- 
sels, as  in  fig.  80. 

It  is  on  the  principle  of  this  tendency,  that  the  little  in 
strument  called  the  water  level  is  constructed. 

445.  The  form  of  this  Fig.  88. 
instrument  is  represented 

by  fig.  88.  It  consists  of 
a,  b,  a  tube,  with  its  two 
ends  turned  at  right  an- 
gles, and  left  open.  Into  b 


How  is  it  shown  that  the  pressure  of  the  fluid  at  5,  is  equal  to  what 
it  would  have  been  had  the  liquid  been  perpendicular  above  that  point  1 
On  what  principle  is  the  water-level  constructed  1  Describe  the.  man- 
ner in  which  the  level  with  sights  is  used,  and  the  reason  why  the 
floats  will  ahvays  be  at  the  same  height  1 


WATER  LEVEL.  105 

one  of  the  ends  is  poured  water  or  mercury,  until  the  fluid 
rises  a  little  in  the  angles  of  the  tube.  On  the  surface  of  the 
fluid,  at  each  end,  are  then  placed  small  floats,  carrying  up- 
right frames,  across  which  are  drawn  small  wires  or  hairs, 
as  seen  at  c  and  d.  These  hairs  are  called  the  sights,  and 
are  across  the  line  of  the  tube. 

446.  It  is  obvious  that  this  instrument  will  always  indi- 
cate a  level,  when  the  floats  are  at  the  same  height,  in  re- 
spect to  each  other,  and  not  in  respect  to  their  comparative 
heights  in  the  ends  of  the  tube,  for  if  one  end  of  the  instru- 
ment be  held  lower  than  the  other,  still  the  floats  must  al- 
ways be  at  the  same  height.     To  use  this  level,  therefore, 
we  have  only  to  bring  the  two  sights,  so  that  one  will  range 
with  the  other;  and  on  placing  the  eye  at  c,  and  looking 
towards  d,  this  is  determined  in  a  moment. 

This  level  is  indispensable  in  the  construction  of  canals 
and  aqueducts,  since  the  engineer  depends  entirely  on  it,  to 
ascertain  whether  the  water  can  be  carried  over  a  given  hill 
or  mountain. 

447.  The  common  spirit  level  con-  Fig.  89. 
sists  of  a  glass  tube,   fig.  89,    filled  ^ 

with  spirit  of  wine,  excepting  a  small     u    ^^m-m^^p    i 

space  in  which  there  is  left  a  bubble     « ' 

of  air.     This  bubble,    when  the   in- 
strument is  laid  on  a  level  surface,  will  be  exactly  in  the 
middle  of  the  tube,  and  therefore  to  adjust  a  level,  it  is  only 
necessary  to  bring  the  bubble  to  this  position. 

The  glass  tube  is  enclosed  in  a  brass  case,  which  is  cut 
out  on  the  upper  side,  so  that  the  bubble  may  be  seen,  as 
represented  in  the  figure. 

448.  This  instrument  is  employed  by  builders  to  leve* 
their  work,  and  is  highly  convenient  for  that  purpose,  since 
it  is  only  necessary  to  lay  it  on  a  beam  to  try  its  level. 

449.  Improved  Water  Level. — In  this  edition  we  add 
the  figure  and  description  of  a  more  complete  Water  Level 
than  that  seen  at  fig.  88. 

What  is  the  use  of  the  level  7  Describe  the  common  spirit  level,  and 
the  method  of  using  it  ? 


WATER  LEVEL. 


Fig.  90. 


106 

950.  Let  A,  fig. 
90,  be  a  straight 
glass  tube,  having 
two  legs,  or  two 
other  glass  tubes, 
rising  from  each  end 
at  right  angles.  Let 
the  tube  A,  and  a 
part  of  the  legs,  be 
filled  with  mercury, 
or  some  other  liquid, 
and  on  the  surfaces, 
a  b,  of  the  liquid,  let 
floats  be  placed  car- 
rying upright  wires, 
to  the  ends  of  which 
are  attached  sights  at  1,2.  These  sights  are  represented 
by  3,  4,  and  consist  of  two  fine  threads,  or  hairs,  stretched  at 
right  angles  across  a  square,  and  are  placed  at  right  angles 
to  the  length  of  the  instrument. 

451.  They  are  so  adjusted  that  the  points  where  the  hairs 
intersect  each  other,  shall  be  at  equal  heights  above  the 
floats.      This  adjustment  may  be  made  in  the  following 
manner  : 

452.  Let  the  eye  be  placed  behind  one  of  the  sights,  look- 
ing through  it  at  the  other,  so  as  to  make  the  points,  where 
the  hairs  intersect,  cover  each  other,  and  let  some  distant 
object,  covered  by  this  point,  be  observed.      Then  let  the 
instrument  be  reversed,  and  let  the  points  of  intersection  of 
the  hairs  be  viewed  in  the  same  way,  so  as  to  cover  each 
other.     If  they  are  observed  to  cover  the  same  distant  object 
as  before,  they  will  be  of  equal  heights  above  the  surfaces 
of  the  liquid.  But,  if  the  same  distant  points  be  not  observed 
in  the  direction  of  these  points,  then  one  or  the  other  of  the 
sights  must  be  raised  or  lowered,  by  an  adjustment  provided 
for  that  purpose,  until  the  points  of  intersection  be  brought 
to  correspond.     These  points  will  then  be  properly  adjust- 
ed, and  the  line  passing  through  them  will  be  exactly  hori- 
zontal.    All  points  seen  in  the  direction  of  the  sights  will 
be  on  the  level  of  the  instrument. 

453.  The  principles  on  which  this  adjustment  depends 


Explain,  by  fig.  90,  how  an  exact  line  may  be  obtained  by  adjusting 
the  sights  7 


SPECIFIC  GRAVITY. 


107 


are  easily  explained :  if  the  intersections  of  the  hairs  be  at 
the  same  distance  from  the  floats,  the  line  joining  those 
intersections  will  evidently  be  parallel  to  the  lines  join- 
ing the  surfaces  a,  b,  of  the  liquid,  and  will  therefore  be 
Wei.  But  if  one  of  these  points  be  more  distant  from  the 
floats  than  the  other,  the  line  joining  the  intersections  will 
point  upwards  if  viewed  from  the  lower  sight,  and  down- 
wards, if  viewed  from  the  higher  one. 

454.  The  accuracy  of  the  results  of  this  instrument,  will 
be  greatly  increased  by  lengthening  the  tube  A. 

SPECIFIC  GRAVITY. 

455.  If  a  tumbler  be  filled  with  water  to  the  brim,  and 
an  egg,  or  any  other  heavy  solid,  be  dropped  into  it,  a  quan- 
tity of  the  fluid,  exactly  equal  to  the  size  of  the  egg,  or  other 
solid,  will  be  displaced,  and  will  flow  over  the  side  of  the 
vessel.     Bodies  which  sink  in  water,  therefore,  displace  a 
quantity  of  the  fluid  equal  to  their  own  bulks. 

456.  Now,  it  is  found,  by  experiment,  that  when  any 
solid  substance  sinks  in  water,  it  loses,  while  in  the  fluid,  a 
portion  of  its  weight,  just  equal  to  the  weight  of  the  bulk  of 
water  which  it  displaces.     This  is  readily  made  evident  bv 
experiment. 

457.  Take   a   piece   of  Fig.  91. 
ivory,  or   any   other  sub- 
stance  that   will    sink  in 

water,  and  weigh  it  accu- 
rately in  the  usual  man- 
ner; then  suspend  it  by  a 
thread,  or  hair,  in  the  emp- 
ty cup  a,  fig.  91,  and  then 
balance  it,  as  shown  in  the 
figure.  Now  pour  water 
into  the  cup,  and  it  will  be 
found  that  the  suspended 
body  will  lose  a  part  of  its  weight,  so  that  a  certain  number 
of  grains  must  be  taken  from  the  opposite  scale,  in  order  to 
make  the  scales  balance  as  before  the  water  was  poured  in. 


When  a  solid  is  weighed  in  water,  why  does  it  lose  a  part  of  its 
weight "?  How  much  less  will  a  cubic  inch  of  any  substance  weigh  in 
water  than  in  air  1  How  is  it  proved  by  fig.  91,  that  a  body  weighs 
less  in  water  than  in  air  ?  What  is  the  specific  gravity  of  a  bodv? 
How  are  the  specific  gravities  of  solid  bodies  taken  7 


108  »*ECIFIC  GRAVITY. 

The  number  of  grains  taken  from  the  opposite  scale,  show 
the  weight  of  a  quantity  of  water  equal  to  the  bulk  of  the 
body  so  suspended. 

458.  It  is  on  the  principle,  that  bodies  weigh  less  in  the 
water  than  they  do  when  weighed  out  of  it,  or  in  the  air, 
that  water  becomes  the  means  of  ascertaining  their  specific 
gravities,  for  it  is  by  comparing  the  weight  of  a  body  in  the 
water,  with  what  it  weighs  out  of  it,  that  its  specific  grav- 
ity is  determined. 

459.  Thus,  suppose  a  cubic  inch  of  gold  weighs  19  ounces, 
and  on  being  weighed  in  water,  weighs  only  18  ounces,  or 
loses  a  nineteenth  part  of  its  weight,  it  will  prove  that  gold, 
bulk  for  bulk,  is  nineteen  times  heavier  than  water,  and  thus 
19  would  be  the  specific  gravity  of  gold.     And  so  if  a  cube 
of  copper  weigh  9  ounces  in  the  air,  and  only  8  ounces  in 
the  water,  then  copper,  bulk  for  bulk,  is  9  times  as  heavy  as 
water,  and  therefore  has  a  specific  gravity  of  9. 

460.  If  the  body  weigh  less,  bulk  for  bulk,  than  water, 
it  is  obvious,  that  it  will  not  sink  in  it,  and  therefore  weights 
must  be  added  to  the  lighter  body,  to  ascertain  how  much 
less  it  weighs  than  water. 

The  specific  gravity  of  a  body,  then,  is  merely  its  weight, 
compared  with  the  same  bulk  of  water ;  and  water  is  thus 
made  the  standard  by  which  the  weights  of  all  other  bodies 
are  compared. 

461.  To  take  the  specific  gravity  of  a  solid  which  sinks 
in  water,  firsl  weigh  the  body  in  the  usual  manner,  and  note 
down  the  number  of  grains  it  weighs.     Then,  with  a  hair, 
or  fine  thread,  suspend  it  from  the  bottom  of  the  scale-dish, 
in  a  vessel  of  water,  as  represented  by  fig.  91.    As  it  weighs 
less  in  water,  weights  must  be  added  to  the  side  of  the  scale 
where  the  body  is  suspended,  until  they  exactly  balance 
each  other.     Next,  note  down  the  number  of  grains  so  add- 
ed, and  they  will  show  the  difference  between  the  weight 
of  the  body  in  air,  and  in  water. 

It  is  obvious,  that  the  greater  the  specific  gravity  of  the 
body,  the  less,  comparatively,  will  be  this  difference,  because 
each  body  displaces  only  its  own  bulk  of  water,  and  some 
bodies  of  the  same  bulk,  will  weigh  many  times  as  much 
as  others. 

462.  For  example,  we  will  suppose  that  a  piece  of  pla- 
tina,  weighing  22  ounces,  will  displace  an  ounce  of  water, 

Why  does  a  heavy  body  weigh  comparatively  less  in  the  water  tha» 
a  light  one  ? 


HYDROMETER.  109 

while  a  piece  of  silver,  weighing-  22  ounces,  will  displace 
two  ounces  of  water.  The  platina,  therefore,  when  sus- 
pended as  above  described,  will  require  one  ounce  to  make 
the  scales  balance,  while  the  same  weight  of  silver  will  re- 
quire two  ounces  for  the  same  purpose.  The  platina,  there- 
fore, bulk  for  bulk,  will  weigh  twice  as  much  as  the  silver, 
and  will  have  twice  as  much  specific  gravity. 

Having  noted  down  the  difference  between  the  weight  of 
the  body  in  air  and  in  water,  as  above  explained,  the  specific 
gravity  is  found  by  dividing  the  weight  in  air,  by  the  loss  in 
water.  The  greater  the  loss,  therefore,  the  less  will  be  the 
specific  gravity,  the  bulk  being  the  same. 

Thus,  in  the  above  example,  22  ounces  of  platina  was  sup- 
posed to  lose  one  ounce  in  water,  while  22  ounces  of  silver 
lost  two  ounces  in  water.  Now  22,  divided  by  1,  the  loss 
of  the  platina,  is  22;  and  22  divided  by  2,  the  loss  in  the 
silver,  is  11.  So  that  the  specific  gravity  of  platina  is  22, 
while  that  of  silver  is  11.  The  specific  gravities  of  these 
metals  are,  however,  a  little  less  than  here  estimated.  [For 
other  methods  of  taking  specific  gravity,  see  Chemistry.} 

HYDROMETER. 

463.  The  hydrometer  is  an  instrument,  by  which  the  spe- 
cific gravities  of  fluids  are  ascertained,  by  the  depth  to  which 
it  sinks  below  their  surfaces. 

Suppose  a  cubic  inch  of  lead  loses,  when  weighed  in 
water,  253  grains,  and  when  weighed  in  alcohol,  only  209 
grains,  then,  according  to  the  principle  already  recited,  a 
cubic  inch  of  water  actually  weighs  253,  and  a  cubic  inch 
of  alcohol  209  grains,  for  when  a  body  is  weighed  in  fluid, 
it  loses  just  the  weight  of  the  fluid  it  displaces. 

464.  Water,  as  we  have  already  seen,  (460,)  is  the  stand- 
ard by  which  the  weights  of  other  bodies  are  compared,  and 
by  ascertaining  what  a  given  bulk  of  any  substance  weighs 
in  water,  and  then  what  it  weighs  in  any  other  fluid,  the 
comparative  weight  of  water  and  this  fluid  will  be  known. 
For  if,  as  in  the  above  example,  a  certain  bulk  of  water 
weighs  253  grains,  and  the  same  bulk  of  alcohol  only  209 

Having  taken  the  difference  between  the  weight  of  a  body  in  air 
and  in  water,  by  what  rule  is  its  specific  gravity  found  1  Give  the  ex- 
ample stated,  and  show  how  the  difference  between  the  specific  gravi- 
ties of  platina  and  silver  is  ascertained.  What  is  the  hydrometer  1 
Suppose  a  cubic  inch  of  any  substance  weighs  253  grains  less  in  water 
than  in  air,  what  is  the  actual  weight  of  a  cubic  inch  of  water"? 
10 


1 10  HYDROMETER 

grains,  then  alcohol  has  a  specific  gravity,  nearly  one  fourth 
less  than  water. 

It  is  on  this  principle  that  the  hydrometer  is  constructed. 
It  is  composed  of  a  hollow  ball  of  glass,  or  metal,  with  a 
graduated  scale  rising  from  its  upper  part,  and  a  weight 
on  its  under  part,  which  serves  to  balance  it  in  the  fluid. 

Such  an  instrument  is  represented  by  fig.        Fig.  92. 
92,  of  which  b  is  the  graduated  scale,  and  a 
the  weight,  the  hollow  ball  being  between 
them. 

465.  To  prepare  this  instrument  for  use, 
weights,  in  grains,  or  half  grains,  are  put 
into  the  little  ball  a,  until  the  scale  is  carried 
down,  so  that  a  certain  mark  on  it  coincides 
exactly  with  the  surface  of  the  water.    This 
mark,  then,  becomes  the  standard  of  compari- 
son between  water  and  any  other  liquid,  in 
which  the  hydrometer  is  placed.    If  plunged 
into  a  fluid  lighter  than  water,  it  will  sink, 
and  consequent!  y^the  fluid  will  rise  higher 

on  the  scale.  If  the  fluid  is  heavier  than  water,  the  scale 
will  rise  above  the  surface  in  proportion,  and  thus  it  is  as- 
certained, in  a  moment,  whether  any  fluid  has  a  greater  or 
less  specific  gravity  than  water. 

To  know  precisely  how  much  the  fluid  varies  from  the 
standard,  the  scale  is  marked  off  into  degrees,  which  indi- 
cate grains  by  weight,  so  that  it  is  ascertained,  very  exactly, 
how  much  the  specific  gravity  of  one  fluid  differs  from  that 
of  another. 

466.  Water  being  the  standard  by  which  the  weights  of 
other  substances  are  compared,  it  is  placed  as  the  unit,  or 
point  of  comparison,  and  is  therefore  1,  10,  100,  or    1000, 
the  ciphers  being  added  whenever  there  are  fractional  parts 
expressing  the  specific  gravity  of  the  body.     It  is  always 
understood,  therefore,  that  the  specific  gravity  of  water  is  1, 
and  when  it  is  said  a  body  has  a  specific  gravity  of  2,  it  is 
only  meant,  that  such  a  body  is,  bulk .  for  bulk,  twice  as 
heavy  as  water.     If  the  substance  is  lighter  than  water,  it 

On  what  principle  is  the  hydrometer  founded  1  How  is  this  instru- 
ment formed  1  How  is  the  hydrometer  prepared  for  use  1  How  is  it 
known,  by  this  instrument,  whether  the  fluid  is  lighter  or  heavier  than 
water  1  What  is  the  standard  by  which  the  weights  of  other  bodies 
are  compared  1  What  is  the  specific  gravity  of  water?  When  it  is  said 
that  the  specific  gravity  of  a  body  is  2,  or  4,  what  meaning  is  intended 
to  be  conveyed  ? 


SYPHON.  Ill 

has  a  specific  gravity  of  0,  with  a  fractional  part.  Thus 
alcohol  has  a  specific  gravity  of  0,809,  that  is,  809,  water 
being  1000.  * 

By  means  of  this  instrument,  it  can  he  told  with  great  ac- 
curacy, how  much  water  has  been  added  to  spirits,  for  the 
greater  the  quantity  of  water,  the  higher  will  the  scale  rise 
above  the  surface. 

The  adulteration  of  milk  with  water,  can  also  he  readily 
detected  with  it,  for  as  new  milk  has  a  specific  gravity  of 
1032,  water  being  1000,  a  very  small  quantity  of  water  mix- 
ed with  it  would  be  indicated  by  the  instrument. 

THE  SYPHON. 

467.  Take  a  tube,  bent  like  .the  letter  U,  and  having  filled 
it  with  water,  place  a  finger  on  each  end,  and  in  this  state 
plunge  one  of  the  ends  into  a  vessel  of  water,  so  that  the 
end  Fn  the  water  shall  be  a  little  the  highest,  then  remove 
the  fingers,  and  the  liquid  will  flow  out,  and  continue  to  do 
so,  until  the  vessel  is  exhausted. 

A  tube  acting  in  this  manner,  is  called  a  syphon,  and  is 
represented  by  fig.  93.  The  reason  why  the  water  flows 
from  the  end  of  the  tube  a,  and, 
consequently,  ascends  through 
the  other  part,  is,  that  there  is  a 
greater  weight  of  the  fluid  from 
b  to  a,  than  from  c  to  Z>,  because 
the  perpendicular  height  from  b 
to  a  is  the  greatest.  The  weight 
of  the  water  from  b  to  a  falling 
downwards,  by  its  gravity,  tends 
to  form  a  vacuum,  or  void  space, 
in  that  leg  of  the  tube;  but  the 
pressure  of  the  atmosphere  on  the 
water  in  the  vessel,  constantly  forces  the  fluid  up  the  other 
leg  of  the  tube,  to  fill  the  void  space,  and  thus  the  stream  is 
continued  as  long  as  any  water  remains  in  the  vessel. 

468.  Intermitting  Springs. — The  action  of  the  syphon 
depends  upon  the  same  principle  as  the  action  of  the  pump, 
namely,  the  pressure  of  the  atmosphere,  and  therefore  its  ex- 
planation properly  belongs  to  Pneumatics.     It  is  introduced 

Alcohol  has  a  specific  gravity  of  809  ;  what,  in  reference  to  this,  is 
the  specific  gravity  of  water  1  In  what  manner  is  a  syphon  made  1 
Explain  the  reason  why  the  water  ascends  through  one  leg  of  the  sy- 
phoa,  and  descends  through  the  other.  What  is  an  intermittent  spring  1 


J12 


SYPHON. 


here  merely  for  the  purpose  of  illustrating  the  phenomena 
of  intermitting  springs;  a  subject  which  properly  belongs 
to  Pneumatics. 

Some  springs,  situated  on  the  sides  of  mountains,  flow  for 
a  while  with  great  violence,  and  then  cease  entirely.  After 
a  time,  they  begin  to  flow  again,  and  then  suddenly  stop,  as 
before.  These  are  called  intermitting  springs.  Among 
ignorant  and  superstitious  people,  these  strange  appearances 
have  been  attributed  to  witchcraft,  or  the  influence  of  some 
supernatural  power.  But  an  acquaintance  with  the  laws  of 
nature  will  dissipate  such  ill  founded  opinions,  by  showing 
that  they  owe  their  peculiarities  to  nothing  more  than  natu- 
ral syphons,  existing  in  the  mountains  from  whence  the 
water  flows. 

Fig.  94. 


469.  Fig.  94  is  the  section  of  a  mountain  and  spring, 
showing  how  the  principle  of  the  syphon  operates  to  pro- 
duce the  effect  described.  Suppose  there  is  a  crevice,  or 
hollow  in  the  rock  from  a  to  b,  and  a  narrow  fissure  lead 
ing  from  it,  in  the  form  of  the  syphon,  b  c.  The  water,  from 
the  rills  f  e,  filling  the  hollow,  up  to  the  line  a  d,  it  will 
then  discharge  itself  through  the  syphon,  and  continue  to 
run  until  the  water  is  exhausted  down  to  the  leg  of  the  sy- 
phon b,  when  it  will  cease.  Then  the  water  from  the  rills 
continuing  to  run  until  the  hollow  is  again  filled  up  to  the 
same  line,  the  syphon  again  begins  to  act,  and  again  dis- 
charges the  contents  of  the  reservoir  as  before,  and  thus  the 
spring  p,  at  one  moment,  flows  with  great  violence,  and  the 
next  moment  ceases  entirely. 

How  is  the  phenomenon  of  the  intermittent  spring  explained  1  Ex- 
plain fig.  94,  and  show  the  reason  why  such  a  spring  will  flow,  and 
cease  to  flow,  alternately. 


HYDRAULICS.  113 

The  hollow,  above  the  line  a  d,  is  supposed  not  to  be  fill- 
ed with  the  water  at  all,  since  the  syphon  begins  to  ict 
whenever  the  fluid  rises  up  to  the  bend  d. 

During  the  dry  seasons  of  the  year,  it  is  obvious,  that 
such  a  spring  would  cease  to  flow  entirely,  and  would  be 
gin  again  only  when  the  w^ter  from  the  mountain  filled  the 
cavity  through  the  rills. 

Such  springs,  although  not  very  common,  exist  in  various 
parts  of  the  world.  Dr.  Atwell  has  described  one  in  the 
'Philosophical  Transactions,  which  he  examined  in  Devon- 
shire, in  England.  The  people  in  the  neighbourhood,  as 
usual,  ascribed  its  actions  to  some  sort  of  witchery,  and  ad- 
vised the  doctor,  in  case  it  did  not  ebb  and  flow  readily, 
when  he  and  his  friend  were  both  present,  that  one  of  them 
should  retire,  and  see  what  the  spring  would  do,  when  only 
the  other  was  present. 


HYDRAULICS. 

470.  It  has  been  stated,  (398,)  that  Hydrostatics  is  that 
branch  of  Natural  Philosophy,  which  treats  of  the  weight, 
pressure,  and  equilibrium  of  fluids,  and  that  Hydraulics  has 
for  its  object  the  investigation  of  the  laws  which  regulate 
fluids  in  motion. 

If  the  pupil  has  learned  the  principles  on  which  the  press- 
ure and  equilibrium  of  fluids  depend,  as  explained  under 
the  former  article,  he  will  now  be  prepared  to  understand 
the  laws  which  govern  fluids  when  in  motion. 

Tb*^  pressure  of  water  downwards,  is  exactly  in  the  same 
proportion  to  its  height,  as  is  the  pressure  of  solids  in  the 
same  direction. 

471.  Suppose  a  vessel  of  three  inches  in  diameter  has  a 
billft  of  wood  set  up  in  it,  so  as  to  touch  only  the  bottom, 
and  suppose  the  piece  of  wood  to  be  three  feet  long,  and  to 
\vei  (h  nine  pounds;  then  the  pressure  on  the  bottom  of  the 
vessel  will  be  nine  pounds.     If  another  billet  of  wood  be 
set  on  this,  of  the  same  dimensions,  it  will  press  on  its  top 
with  the  weight  of  nine  pounds,  and  the  pressure  at  t^e  bot- 
tom will  be  18  pounds,  and  if  another  billet  be  set  on  vhis. 

How  does  the  science  of  Hydrostatics  differ  from  that  of  Hydrau- 
lics 1  Does  the  downward  pressure  of  water  differ  from  the  downward 
pressure  of  solids,  in  proportio"  7  How  is  the  downward  pressure  of 
water  illustrated  1 

10* 


114  HYDRAULICS. 

the  pressure  at  the  bottom  will  be  27  pounds,  and  so  on,  in 
this  ratio,  to  any  height  the  column  is  carried. 

472.  Now  the  pressure  of  fluids  is  exactly  in  the  same 
proportion ;  and  when  confined  in  pipes,  may  be  considered 
as  one  short  column  set  on  another,  each  of  which  increases 
the  pressure  of  the  lowest,  in  proportion  to  their  number  and 
height. 

473.  Thus,  notwithstanding  the  lateral  press-     FL5- 
ure  of  fluids,  their  downward  pressure  is  as  their 
height.     This  fact  will  be  found  of  importance 

in  the  investigation  of  the  principles  of  certain 
hydraulic  machines,  and  we  have,  therefore,  en- 
deavoured to  impress  it  on  the  mind  of  the  pupil 
by  fig.  95,  where  it  will  be  seen,  that  if  the 
pressure  of  three  feet  of  water  be  equal  to  nine 
pounds  on  the  bottom  of  the  vessel,  the  pressure 
of  twelve  feet  will  be  equal  to  thirty-six  pounds. 

474.  The  quantity  of  water  which  will  be  dis- 
charged from  an  orifice  of  a  given  size,  will  be 


27 


in  proportion  to  the  height  of  the  column  of 
water  above  it,  for  the  discharge  will  increase  in 
velocity  in  proportion  to  the  pressure,  and  the 
pressure,  we  have  already  seen ,  will  be  in  a 
fixed  ratio  to  the  height. 

475.  If  a  vessel,  fig.  96,  Fig.  96. 

be  filled  with  water,  and 
three  apertures  be  made  in 
its  sides  at  the  points  a,  b% 
and  c,  the  fluid  will  be 
thrown  out  in  jets,  and  will 
fall  towards  the  earth,  in 
the  curved  lines,  a,  b,  and 
c.  The  reason  why  these 
curves  differ  in  shape,  is, 
that  the  fluid  is  acted  on  by 
two  forces,  namely,  the 
pressure  of  the  water  above  the  jet,  which  produces  its  velo- 
city forward,  and  the  action  of  gravity,  which  impels  it 
downward.  It  therefore  obeys  the  same  laws  that  solids  do 

Without  reference  to  the  lateral  pressure,  in  what  proportion  do 
fluids  press  downwards  1  What  will  be  the  proportion  of  a  fluid  dis- 
charged from  an  orifice  of  a  given  size  1  Why  do  the  lines  described 
by  the  jets  from  the  vessel,  fig.  96,  differ  in  shape! 


HYDRAULICS.  116 

when  projected  forward,  and  falls  down  in  curved  lines,  the 
shapes  of  which  depend  on  their  relative  velocities. 

The  quantity  of  water  discharged,  being  in  proportion  to 
the  pressure,  that  discharged  from  each  orifice  will  differ  in 
quantity  according  to  the  height  of  the  water  above  it. 

476.  It  is  found,  however,  that  the  velocity  with  which  a 
vessel  discharges  its  contents,  does  not  depend  entirely  on 
the  pressure,  but  in  part  on  the  kind  of  orifice  through  which 
the  liquid  flows.     It  might  be  expected,  for  instance,  that  a 
tin  vessel  of  a  given  capacity,  with  an  orifice  of  say  an  inch 
in  diameter  through  its  side,  would  part  with  its  contents 
sooner  than  another  of  the  same  capacity  and  orifice,  whose 
side  was  an  inch  or  two  thick,  since  the  friction  through  the 
tin  might  be  considered  much  less  than  that  presented  by 
the  other  orifice.     But  it  has  been  found,  by  experiment, 
that  the  tin  vessel  does  not  part  with  its  contents  so  soon  as 
another  vessel,  of  the  same  height  and  size  of  orifice,  from 
which  the  water  flowed  through  a  short  pipe.     And,  on 
varying  the  length  of  these  pipes,  it  is  found  that  the  most 
rapid  discharge,  other  circumstances  being  equal,  is  through 
a  pipe,   whose  length  is  twice  the  diameter  of  its  orifice. 
Such  an  aperture  discharged  82  quarts,  in  the  same  time 
that  another  vessel  of  tin,  without  the  pipe,  discharged  62 
quarts. 

This  surprising  difference  is  accounted  for,  by  supposing 
that  the  cross  currents,  made  by  the  rushing  of  the  water 
from  different  directions  towards  the  orifice,  mutually  inter- 
fere with  each  other,  by  which  the  whole  is  broken,  and 
thrown  into  confusion  by  the  sharp  edge  of  the  tin,  and 
hence  the  water  issues  in  the  form  of  spray,  or  of  a  screw, 
from  such  an  orifice.  A  short  pipe  seems  to  correct  this 
contention  among  opposing  currents,  and  to  smooth  the 
passage  of  the  whole,  and  hence  we  may  observe,  that  from 
such  a  pipe,  the  stream  is  round  and  well  defined. 

477.  Proportion  between  the  pressure  and  the  velocity  of 
discharge. — If  a  small  orifice  be  made  in  the  side  of  a  ves- 

What  two  forces  act  upon  the  fluid  as  it  is  discharged,  and  how  do 
these  forces  produce  a  curved  line  1  Does  the  velocity  with  which  a 
fluid  is  discharged,  depend  entirely  on  the  pressure  1  What  circum- 
stance, besides  pressure,  facilitates  the  discharge  of  water  from  an  ori- 
ncel  In  a  tube  discharging  water  with  the  greatest  velocity,  what  is 
the  proportion  between  its  diameter  and  its  length  1  What  is  the  pro- 
portion between  the  quantity  of  fluid  discharged  through  an  orifice  of 
tin,  and  through  a  short  pipe1? 


I  10  HYDRAULICS. 

sel  filled  with  any  liquid,  the  liquid  will  flow  out  with  a 
force  and  velocity,  equal  to  the  pressure  which  the  liquid 
before  exerted  on  that  portion  of  the  side  of  the  vessel  be- 
fore the  orifice  was  made. 

Now,  as  the  pressure  of  fluids  is  as  their  heights,  it  fol- 
lows,  as  above  stated,  that  if  several  such  orifices  are  made, 
the  lowest  will  discharge  the  greatest,  while  the  highest 
will  discharge  the  least,  quantity  of  the  fluid. 

478.  The  velocity  of  discharge,  in  the  several  orifices  of 
such  a  vessel,  will  show  a  remarkable  coincidence  between 
the  ratio  of  increase  in  the  quantity  of  liquid,  and  the  in- 
creased velocity  of  a  falling  body  (82.) 

Thus,  if  the  tall  vessel,  fig.  97,  of  equal,  Fig.  97. 
dimensions  throughout,  be  filled  with  wa- 
ter, and  a  small  orifice  be  made  at  one 
inch  from  the  top,  or  below  the  surface,  as 
at  1  ;  and  another  at  2,  4  inches  below 
this;  another  at  9  inches,  a  fourth  at  16 
inches ;  and  a  fifth  at  25  inches  ;  then  the 
velocities  of  discharge,  from  these  several 
orifices,  will  be  in  the  proportion  of  1,2, 
3,  4,  5. 

To  express  this  more  obviously,  we  will 
place  the  expressions  of  the  several  veloci- 
ties in  the  upper  line  of  the  following  ta- 
ble, the  lower  numbers,  corresponding, 
expressing  the  depths  of  the  several) 
orifices. 


Velocity, 
Depth, 

1 

2 
4 

3 
9 

4 
16 

5 

25 

6 
36 

7 
49 

8 
64 

9 

81 

10 

100  j 

479.  Thus  it  appears,  that  to  produce  a  twofold  velocity 
a  fourfold  height  is  necessary.      To  obtain  a  threefold  V9 
locity  of  discharge,  a  ninefold  height  is  required,  and  for  ? 
fourfold  velocity,  sixteen  times  the  height  is  necessary,  an*1 
so  in  this  proportion,  as  shown  by  the  table.     (See  86.) 

480.  To  apply  this  law  to  the  motion  of  falling  bodies,  it 
appears  that  if  a  body  were  allowed  to  fall  freely  from  the 
surface  of  the  water  downwards,  being  unobstructed  by  the 
fluid,  it  would,  on  arriving  at  each  of  the  orifices,  have  ve- 
locities proportional  to  those  of  the  water  discharged  at  the 


What  are  the  proportions  between  the  velocities  of  discharge  arid  th* 
heights  of  the  orifices,  as  above  explained  ? 


HYDRAULICS.  117 

said  orifices  respectively.  Thus,  whatever  velocity  it  would 
have  acquired  on  arriving  at  1,  the  first  orifice,  it  would 
have  doubled  that  velocity  on  arriving  at  2,  the  second  ori- 
fice, trebled  it  on  arriving  at  the  third  orifice,  and  so  on 
with  respect  to  the  others. 

481.  In  order  to  establish  the  remarkable  fact,  that  the 
velocity  with  which  a  liquid  spouts  from  an  orifice  in  a  ves- 
sel, is  equal  to  the  velocity  which  a  body  would  acquire  in 
falling  unobstructed  from  the  surface  of  the  liquid  to  the 
depth  of  the  orifice,  it  is  only  necessary  to  prove  the  truth  of 
the  principle  in  any  one  particular  case. 

482.  Now  it  is  manifestly  true,  if  the  orifices  be  presented 
downwards,  and  the  column  of  fluid  over  it  be  of  small 
height,  then  tnis  indefinitely  small  column  will  drop  out  of 
the  orifice  by  the  mere  effect  of  its  own  weight,  and,  there- 
fore, with  the  same  velocity  as  any  other  falling  body  ;  but 
as  fluids  transmit  pressure  in  all  directions,  the  same  effect 
will  be  produced  whatever  may  be  the  direction  of  the  ori- 
fice.    Hence,  if  this  principle  be  true,  then  the  direction 
and  size  of  the  orifice  can  make  no  difference  in  the  result, 
so  that  the  principle,  above  explained,  follows  as  an  incon- 
trovertible fact. 

FRICTION  BETWEEN  SOLIDS  AND  FLUIDS. 

483.  The  rapidity  with  which  water  flows  through  pipes 
of  the  same  diameter,  is  found  to  depend  much  on  the  nature 
of  their  internal  surfaces.     Thus  a  lead  pipe,  with  a  smooth 
aperture,  under  the  same  circumstances,  will  convey  much 
more  water  than  one  of  wood,  where  the  surface  is  rough, 
or  beset  with  points.     In  pipes,  even  where  the  surface  is 
as  smooth  as  glass,  there  is  still  considerable  friction,  for  in 
all  cases,  the  water  is  found  to  pass  more  rapidly  in  the 
middle  of  the  stream  than  it  does  on  the  outside,  where  it 
rubs  against  the  sides  of  the  tube. 

The  sudden  turns,  or  angles  of  a  pipe,  are  also  found  to 
be  a  considerable  obstacle  to  the  rapid  conveyance  of  the 
water,  for  such  angles  throw  the  fluid  into  eddies  or  cur- 
rents, by  which  its  velocity  is  arrested. 

In  practice,  therefore,  sudden  turns  are  generally  avoid- 
How  is  it  proved  that  the  velocity  of  the  spouting  liquid  is  equal  to 
that  of  a  falling  body  1  Suppose  a  lead  and  a  glass  tube,  of  the  same 
diameter,  which  will  delivpr  the  greatest  quantity  of  liquid  in  the  same 
time  1  Why  will  a  glass  tuoe  deliver  most  7  What  is  said  of  the  sud- 
den turnings  of  a  tube  in  retarding  the  motion  of  the  fluid  7 


118  HYDRAULICS. 

ea,  and  where  it  is  necessary  that  the  pipe  should  change 
its  direction,  it  is  done  by  means  of  as  large  a  circle  as  con- 
venient. 

Where  it  is  proposed  to  convey  a  certain  quantity  of 
water  to  a  considerable  distance  in  pipes,  there  will  be  a 
great  disappointment  in  respect  to  the  quantity  actually  deli- 
vered, unless  the  engineer  takes  into  account  the  friction, 
and  the  turnings  of  the  pipes,  and  makes  large  allowances 
for  these  circumstances.  If  the  quantity  to  be  actually  de- 
livered ought  to  fill  a  two  inch  pipe,  one  of  three  inches 
will  not  be  too  great  an  allowance,  if  the  water  is  to  be  con 
veyed  to  any  considerable  distance. 

In  practice,  it  will  be  found  that  a  pipe  of  two  inches  in 
diameter,  one  hundred  feet  long,  will  discharge  about  five 
times  as  much  water  as  one  of  one  inch  in  diameter  of  the 
same  length,  and  under  the  same  pressure.  This  difference 
is  accounted  for,  by  supposing  that  both  tubes  retard  the  mo- 
tion of  the  fluid,  by  friction,  at  equal  distance  from  their  in- 
ner surfaces,  and  consequently,  that  the  effect  of  this  cause 
is  much  greater  in  proportion,  in  a  small  tube,  than  in  » 
large  one. 

484.  The  effect  of  friction  in  retarding  the  motion  of 
fluids  is  perpetually  illustrated  in  the  flowing  of  rivers  and 
brooks.      On   the   side  of  a   river,  the  water,  especially 
where  it  is  shallow,  is  nearly  still,  while  in  the  middle  of 
the  stream  it  may  run  at  the  rate  of  five  or  six  miles  an 
hour.     For  the  same  reason,  the  water  at  the  bottoms  of 
rivers  is  much  less  rapid  than  at  the  surface.     This  is  often 
proved  by  the  oblique  position  of  floating  substances,  which 
in  still  water  would  assume  a  vertical  direction. 

485.  Thus,  suppose  the  stick  of  wood         Fig.  98. 
e,  fig.  98,  to  be  loaded  at  one  end  with  _ 

lead,  of  the  same  diameter  as  the  wood,  ffi 
so  as  to  make  it  stand  upright  in  still  | 
water.     In  the  current  of  a  river,  where  j 
the  lower  end  nearly  reaches  the  hot-      ^ 
torn,  it  will  incline  as  in  the  figure,  her  j 
cause  the  water  is  more  rapid  towards  { 
the  surface  than  at  the  bottom,  and  hence 
the  tendency  of  the  upper  end  to  move 


faster  than  the  lower  one,  gives  it  an  inclination  forward. 

How  much  more  water  will  a  two  inch  tube  of  a  hundred  feet  long 
discharge,  than  a  one  inch  tube  of  the  same  length  1  How  is  this  di£ 
Terence  accounted  for  1  How  do  rivers  show  the  effect  of  friction  in  re- 
tarding the  motion  of  their  water*?  Explain  fig.  98 


HYDRAULICS. 


119 


MACHINES  FOR  RAISING  WATER. 

486.  The  common   pump,  though  a  hydraulic  machine, 
depends  on  the  pressure  of  the  atmosphere  for  its  effect,  and 
therefore  its  explanation  comes  properly  under  the  article 
Pneumatics,  where  the  consequences  of  atmospheric  press- 
ure will  be  illustrated. 

Such  machines  only,  as  raise  water  without  the  assist- 
ance of  the  atmosphere,  come  properly  under  the  present 
article. 

487.  Archimedes1  Screw. — Among  these,  one  of  the  most 
curious,  as  well  as  ancient  machines,  is  the  screw  of  Archi- 
medes, and  which  was  invented  by  that  celebrated  philoso- 
pher, two  hundred  years  before  the  Christian  era,  and  then 
employed  for  raising  water  and  draining  land  in  Egypt. 


Fig.  99. 


488.  It  consists  of  a  large  tube,  fig.  99,  coiled  round  a 
shaft  of  wood  to  keep  it  in  place,  and  give  it  support.  Both 
ends  of  the  tube  are  open,  the  lower  one  being  dipped  into 
the  water  to  be  raised,  and  the  upper  one  discharging  it  in 
an  intermitting  stream.  The  shaft  turns  on  a  support  at 
each  end,  that  at  the  upper  end  being  seen  at  a,  the  lower 
one  being  hid  by  the  water.  As  the  machine  now  stands, 
the  lower  bend  of  the  screw  is  filled  with  water,  since  it  is 
below  the  surface  c,  d.  On  turning  it  by  the  handle,  from 
left  to  right,  that  part  of  the  screw  now  filled  with  water  will 
nse  above  the  surface  c,  d,  and  the  water  having  no  place 


Who  is  said  to  have  been  the  inventor  of  Archimedes'  screw  7  Ex- 
plain this  machine,  as  represented  in  fig-.  99,  and  show  how  the  water 
is  elevated  by  turning  it 


120  HYDRAULICS. 

to  escape,  falls  into  the  next  lowest  part  of  the  screw  at  e 
At  the  next  revolution,  that  portion  which,  during-  the  lasf 
was  at  e,  will  be  elevated  to  g,  for  the  lowest  bend  will  re 
ceive  another  supply,  which  in  the  mean  time  will  be  trans- 
ferred to  e,  and  thus,  by  a  continuance  of  this  motion,  the 
water  is  finally  elevated  to  the  discharging  orifice  p. 

This  principle  is  readily  illustrated  by  winding-  a  piece  of 
lead  tube  round  a  walking  stick,  and  then  turning  the  whole 
with  one  end  in  a  dish  of  water,  as  shown  in  the  figure. 

489.  Theory  of  Archimedes'  Screw. — By  the  following 
cuts  and  explanations,  the  manner  in  which  this  machine 
acts  will  be  understood. 

490.  Suppose  Fig.  100. 
the  extremity   1, 

fig.  100,  to  be 
presented  up- 
wards, as  in  the 
figure,  the  screw 
itself  being  in- 
clined as  repre- 
sented. Then, 
from  its  peculiar 
form  and  position, 
it  is  evident,  that  commencing  at  1,  the  screw  will  descend 
until  we  arrive  at  a  certain  point  2  ;  in  proceeding  from  2 
to  3  it  will  ascend.  Thus,  2  is  a  point  so  situated  that  the 
parts  of  the  screw  on  both  sides  of  it  ascend,  and  therefore  if 
any  body,  as  a  ball,  were  placed  in  the  tube  at  2,  it  could  not 
move  in  either  direction  without  ascending.  Again,  the 
point  3,  is  so  situated,  that  the  tube  on  each  side  of  it  de- 
scends ;  and  as  we  proceed  we  find  another  point  4,  which, 
like  2,  is  so  placed,  that  the  tube  on  both  sides  of  it  ascends, 
and,  therefore,  a  body  placed  at  4,  could  not  move  without 
ascending.  In  like  manner,  there  is  a  series  of  other 
points  along  the  lube,  from  which  it  either  descends  or  ascends, 
as  is  obvious  by  inspection. 

491.  Now  let  us  suppose  a  ball,  less  in  size  than  the  bore 
of  the  tube,  so  as  to  move  freely  in  it,  to  be  dropped  in  at  1, 
As  the  tube  descends  from  1  to  2,  the  ball  of  course  will  de- 
scend down  to  2,  where  it  will  remain  at  rest. 


How  may  the  principle  of  Archimedes'  screw  be  readily  illustrated  1 
Explain  the  manner  in  which  a  ball  would  ascend,  fig.  100,  by  turn- 
ittg  the  screw. 


HYDRAULICS.  121 

Next,  suppose  the  ball  to  be  fastened  to  the  tube  at  i',,  and 
suppose  the  screw  to  be  turned  nearly  half  round,  so  that  the 
end  1  shall  be  turned  do\vn\vards,  and  the  point  2  brought 
nearly  to  the  highest  point  of  the  curve  1,  2,  3. 

492.  This  movement  of  the  spiral,  it  is  evident,  would 
change  the  positions  of  the  ascending  and  descending  parts, 
as  represented  by  fig.  101. 

The    ball,    which    we  Fig.  101. 

supposed  attached  to  the 
iube,  is  now  nearly  at  the 
highest  point  at  2,  and  if  • 
detached  will  descend 
down  to  3,  where  it  will 
rest.  The  point  at  which 
2  was  placed  in  the  first 
position  of  the  screw  is 
marked  by  b ,  in  the  second 
position.  The  effect  of 
turning  the  screw,  there- 
fore, will  be  to  transfer  -C 
the  ball  from  the  highest  to  the  lowest  point.  Another  half 
turn  of  the  screw,  will  cause  the  ball  to  pass  over  another 
high  point,  and  descend  the  declivity  down  to  5,  in  fig.  101, 
where  it  will  again  rest. 

493.  It  is  unnecessary  to  explain  the  steps  by  which  the 
ball  would  gain  another  point  of  elevation,  since  it  is  clear 
that  by  continuing  the  same  process  of  action,  and  of  reason- 
ing, it  would  be  plain  that  the  ball  would  be  gradually 
transferred   from   the   lowest   to   the  highest  point  of  the 
screw. 

Now  all  that  we  have  said  with  respect  to  the  ball,  would 
be  equally  true  of  a  drop  of  water  in  the  tube ;  and,  there- 
fore, if  the  extremity  of  the  tube  were  immersed  in  water, 
so  that  the  fluid,  by  its  pressure  or  weight,  be  continually 
forced  into  the  extremity  of  the  screw,  it  would,  by  making- 
it  revolve,  be  gradually  carried  along  the  spiral  to  any 
height  to  which  it  might  extend. 

494.  It  will,  however,  be  seen,  from  the  above  explana- 
tion, that  the  tube  must  not  be  so  elevated  from  the  point  of 
immersion,  that  the  spirals  will  not  descend  from  one  point 
to  another,  in  which  case  it  is  obvious  that  the  machine 


What  is  said  concerning  the  inclination  of  the  tube,  in  order  to  in- 
sure its  action  1 

II 


122 


HYDRAULICS. 


will  not  act.  If  the  tube  be  placed  in  a  perpendicular  posi- 
tion, the  ball,  instead  of  gaming  an  increased  elevation  by 
turning  the  screw,  would  descend  to  the  ground.  A  certain 
inclination,  therefore,  depending  on  the  course  of  the  screw, 
must  be  given  this  machine,  in  order  to  ensure  its  action. 

495.  Instead  of  this  method,  water  was          Fig.  102. 
sometimes    raised    by   the    ancients,   by 

means  of  a  rope,  or  bundle  of  ropes,  as 
shown  at  fig.  102. 

This  mode  illustrates,  in  a  very  strik- 
ing manner,  the  force  of  friction  between 
a  solid  and  fluid,  for  it  was  by  this  force 
alone,  that  the  water  was  supported  and 
elevated. 

496.  The  large  wheel  a,  is  supposed 
to  stand  over  the  well,  and  b,  a  smaller 
wheel,  is  fixed  in  the  water.     The  rope 
is  extended  between  the  two  wheels,  and 
rises  on  one  side  in  a  perpendicular  direc- 
tion.   On  turning  the  wheel  by  the  crank 

d,  the  water  is  brought  up  by  the  friction  of  the  rope,  and 
falling  into  a  reservoir  at  the  bottom  of  the  frame  which 
supports  the  wheel,  is  discharged  at  the  spout  d. 

It  is  evident  that  the  motion  of  the  wheel,  and  conse- 
quently that  of  the  rope,  must  be  very  rapid,  in  order  to 
raise  any  considerable  quantity  of  water  by  this  method.  But 
when  trie  upward  velocity  of  the  rope  is  eight  or  ten  feet 
per  second,  a  large  quantity  of  water  may  be  elevated  to  a 
considerable  height  by  this  machine. 

497.  Barker's  Mill. — For  the  different  modes  of  apply- 
ing water  as  a  power  for  driving  mills,  and  other  useful 
purposes,  we  must  refer  the  reader  to  works  on  practical 
mechanics.     There  is,  however,  one  method  of  turning  ma- 
chinery by  water,  invented  by  Dr.  Barker,  which  is  strictly 
a  philosophical,  and  at  the  same  time  a  most  curious  inven- 
tion, and  therefore  is  properly  introduced  here. 


Explain  in  what  manner  water  is  raised  by  the  machine  represented 
by  fig.  102. 


HYDRAULICS. 


123 


498.    This   machine   is   called  Fig.  103. 

Barkers   centrifugal    mill,    and . H_d 

such  parts  of  it  as  are  necessary  to 
understand  the  principle  on  which 
it  acts  are  represented  by  fig. 
103. 

The  upright  cylinder  a,  is  a 
tube  which  has  a  funnel  shaped 
mouth,  for  the  admission  of  the 
stream  of  water  from  the  pipe  b. 
This  tube  is  six  or  eight  inches  in 
diameter,  and  may  be  from  ten  to 
twenty  feet  long.  The  arms  n 
and  o,  are  also  tubes  communicat- 
ing freely  with  the  upright  one, 
from  the  opposite  sides  of  which 
they  proceed.  The  shaft  d,  is 
firmly  fastened  to  the  inside  of  the 
tube,  openings  at  the  same  time 
being  left  for  the  water  to  pass  to 

the  arms  o  and  n.  The  lower  part  of  the  tube  is  solid,  and 
turns  on  a  point  resting  on  a  block  of  stone  or  iron,  c. 
The  arms  are  closed  at  their  ends,  near  which  are  the  ori- 
fices on  the  sides  opposite  to  tach  other,  so  that  the  water 
spouting  from  them,  will  fly  in  opposite  directions.  The 
stream  from  the  pipe  b,  is  regulated  by  a  stopcock,  so  as  to 
keep  the  tube  a  constantly  full  without  overflowing. 

To  set  this  engine  in  motion,  supple  the  upright  tube  to 
be  filled  with  water,  and  the  arms  n  and  0,  to  be  given,  a 
slight  impulse  ;  the  pressure  of  the  water  from  the  perpen- 
dicular column  in  the  large  tube  will  give  the  fluid  the  ve- 
locity of  discharge  at  the  ends  of  the  arms  proportionate  to 
its  height.  The  reaction  that  is  produced  by  the  flowing 
of  the  water  on  the  points  behind  the  discharging  orifice, 
will  continue,  and  increase  the  rotatory  motion  thus  begun. 
After  a  few  revolutions,  the  machine  will  receive  an  addi- 
tional impulse  by  the  centrifugal  force  generated  in  the 
arms,  and  in  consequence  of  this,  a  much  more  violent  and 
rapid  discharge  of  the  water  takes  place,  than  would  occur 
by  the  pressure  of  that  in  the  upright  tube  alone.  The  cen- 
trifugal force,  and  the  force  of  the  discharge  thus  acting 
at  the  same  time,  and  each  increasing  the  force  of  the 


What  is  fig;.  103  intended  to  represent  1    Describe  this  mill. 


124  PNEUMATICS. 

other,  this  machine  revolves  with  great  velocity  and  pro- 
portionate power.  The  friction  which  it  has  to  overcome, 
when  compared  with  that  of  other  machines,  is  very  slight, 
being  chiefly  at  the  point  c,  where  the  weight  of  the  upright 
tube  and  its  contents  is  sustained. 

By  fixing  a  cog  wheel  to  the  shaft  at  d,  motion  may  be 
given  to  any  kind  of  machinery  required. 

499.  Where  the  quantity  of  water  is  small,  but  its  height 
considerable,  this  macbine  maybe  employed  to  great  advan- 
tage, it  being  under  such  circumstances  one  of  the  most 
powerful  engines  ever  invented. 


PNEUMATICS. 

500.  The  term  Pneumatics  is  derived  from  the  Greek 
pneuma,  which  signifies  breath,  or  air.     It  is  that  science 
which   investigates  the  mechanical  properties  of  air,  and 
other  elastic  fluids. 

Under  the  article  Hydrostatics,  (420,)  it  was  stated  that 
fluids  were  of  two  kinds,  namely,  elastic  and  non-elastic, 
and  that  air  and  the  gases  belonged  to  the  first  kind,  while 
water  and  other  liquids  belonged  to  the  second. 

501.  The  atmosphere  which  surrounds  the  earth,  and  in 
which  we  live,  and  a  portion  of  which  we  take  into  our 
lungs  at  every  breath,  is  called  air,  while  the  artificial  pro- 
ducts which  possess  the  same  mechanical  properties,  are 
called  gases. 

When,  therefore,  the  word  air  is  used,  in  what  follows, 
it  will  be  understood  to  mean  the  atmosphere  which  we 
breathe. 

502.  Every  hollow,  crevice,  or  pore,  in  solid  bodies,  not 
filled  with  a  liquid,  or  some  other  substance,  appears  to  be 
filled  with  air  :  thus,  a  tube  of  any  length,  the  bore  of  which 
is  as  small  as  it  can  be  made,  if  kept  open,  will  be  filled 
with  air ;  and  hence,  when  it  is  said  that  a  vessel  is  filled 
with  air,  it  is  only  meant  that  the  vessel  is  in  its  ordinary 
state.     Indeed,  this  fluid  finds  its  way  into  the  most  minute 
pores  of  all  substances,  and  cannot  be  expelled  and  kept  out 
of  any  vessel,  without  the  assistance  of  the  air-pump,  or 
some  other  mechanical  means. 

503.  By  the  elasticity  of  air,  is  meant  its  spring,  or  the 

What  is  pneumatics  1  What  is  air  1  What  is  gas  7  What  is  meant 
when  it  is  said  that  a  vessel  is  filled  with  air"?  Is  there  any  difficulty  in 
expelling  the  air  from  vessels  ?  What  is  meant  by  the  elasticity  of  air  ? 


PNEUMATICS 


125 


.he  force  with  which  it  re-acts,  when  compressed  in  a  close 
vessel.  It  is  chiefly  in  respect  to  its  elasticity  and  lightness, 
that  the  mechanical  properties  of  air  differ  from  those  of 
water,  and  other  liquids. 

504.  Elastic  fluids  differ  from  each  other  in  respect  to  the 
permanency  of  the  elastic  property.     Thus,  steam  is  elastic 
only  while  its  heat  is  continued,  and  on  cooling,  returns 
again  to  the  form  of  water. 

505.  Some  of  the  gases  also,  on  being  strongly  compress- 
ed, lose  their  elasticity,  and  take  the  form  of  liquids.     But 
air  differs  from  these,  in  being  permanently  elastic ;  that  is, 
if  it  be  compressed  with  ever  so  much  force,  and  retained 
under  compression  for  any  length  of  time,  it  does  not  there- 
fore lose  its  elasticity,  or  disposition  to  reg-am  its  former 
bulk,  but  always  re-acts  with  a  force  in  proportion  to  the 
power  by  which  it  is  compressed. 

506.  Thus,  if  the  strong  tube,  or  barrel,  fig. 
104,  be  smooth,  and  equal  on  the  inside,  and 
there  be  fitted  to  it  the  solid  piston,  or  plug  a, 
so  as  to  work  up  and  down  air  tight,  by  the 
handle  b,  the  air  in  the  barrel  may  be  com- 
pressed into  a  space  a  hundred  times  less  than 
its  usual  bulk.     Indeed,  if  the  vessel  be  of  suf- 
ficient strength,  and  the  force  employed  suffi- 
ciently great,  its  bulk  may  be  lessened  a  thou- 
sand times,  or  in  any  proportion,  according  to 
the  force  employed  ;  and  if  kept  in  this  state  for 
years,  it  will  regain  its  former  bulk  the  instant 
the  pressure  is  removed. 

Thus,  it  is  a  general  principle  in  pneumatics, 
.hat  air  is  compressible  in  proportion  to  the  force 
employed. 

507.  On  the  contrary,  when  the  usual  pressure  of  the  at- 
mosphere is  removed  from  a  portion  of  air,  it  expands  and 
occupies  a  space  larger  than  before;  and  it  is  found  by  ex- 
periment, that  this  expansion  is  in  a  ratio,  as  the  removal  of 
the  pressure  is  more  or  less  complete.     Air  also  expands  or 
increases  in  bulk,  when  heated. 

If  the  stop-cock  c,  fig.  104,  be  opened,  the  piston  a  may 
be  pushed  down  with  ease,  because  the  air  contained  in  the 
barrel  will  be  forced  out  at  the  aperture.     Suppose  the  pis- 
How  does  air  differ  from  steam,  and  some  of  the  gases,  in  respect  to 
its  elasticity  1   Does  air  lose  its  elastic  force  by  being  long  compressed  1 
in  what  proportion  to  the  force  employed  is  the  bulk  of  air  lessened  1 
11* 


_M 


PNEUMATICS. 

ton  to  be  pushed  down  to  within  an  inch  of  the  bottom,  and 
then  the  stop-cock  closed,  so  that  no  air  can  enter  below  it. 
Now,  on  drawing  the  piston  up  to  the  top  of  the  barrel,  the 
inch  of  air  will  expand,  and  fill  the  whole  space,  and  were 
this  space  a  thousand  times  as  large,  it  would  still  be  filled 
with  the  expanded  air,  because  the  piston  removes  the  press- 
ure of  the  external  atmosphere  from  that  within  the  barrel. 
It  follows,  therefore,  that  the  space  which  a  given  portion 
of  air  occupies,  depends  entirely  on  circumstances.  If  it  is 
under  pressure,  its  bulk  will  be  diminished  in  exact  propor- 
tion ;  and  as  the  pressure  is  removed,  it  will  expand  in  pro- 
portion, so  as  to  occupy  a  thousand,  or  even  a  million  times 
as  much  space  as  before. 

508.  Another  property  which  air  possesses  is  weight,  or 
gravity.     This  property,  it  is  obvious,  must  be  slight,  when 
compared  with  the  weight  of  other  bodies.    But  that  air  has 
a  certain  degree  of  gravity  in  common  with  other  ponderous 
substances,  is  proved  by  direct  experiment.    Thus,  if  the  air 
be  pumped  out  of  a  close  vessel,  and  then  the  vessel  be  ex- 
actly weighed,  it  will  be  found  to  weigh  more  when  the  air 
is  again  admitted. 

509.  Pressure  of  the  Atmosphere. — It  is,  however,  the 
weight  of  the  atmosphere  which  presses  on  every  part  of 
the  earth's  surface,  and  in  which  we  live  and  move,  as  in 
an  ocean,  that  here  particularly  claims  our  attention. 

The  pressure  of  the  atmosphere  may  be  easi-    Fig.  105. 
ly  shown  by  the  tube  and  piston,  fig.  105. 

Suppose  there  is  an  orifice  to  be  opened  or 
closed  by  the  valve  b,  as  the  piston  a  is  moved 
up  or  down  in  its  barrel.  The  valve  being  fast- 
ened by  a  hinge  on  the  upper  side,  on  pushing 
the  piston  down,  it  will  open  by  the  pressure  of 
the  air  against  it,  and  the  air  will  make  its  escape. 
But  when  the  piston  is  at  the  bottom  of  the  bar- 
rel, on  attempting  to  raise  it  again,  towards  the 
top,  the  valve  is  closed  by  the  force  of  the  exter- 
nal air  acting  upon  it.  If,  therefore,  the  piston 
be  drawn  up  in  this  state,  it  must  be  against  the 
pressure  of  the  atmosphere,  the  whole  weight  of 

In  what  proportion  will  a  quantity  of  air  increase  in  bulk  as  the 
pressure  is  removed  from  it  7  How  is  thus  illustrated  by  fig.  104 1  On 
what  circumstance,  therefore,  will  the  bulk  of  a  given  portion  of  air 
deoend  1  How  is  it  proved  that  air  has  weight  ?  Explain  in  what 
manner  the  pressure  of  the  atmosphere  is  shown  by  fig.  105. 


AIR  PUMP.  127 

which,  to  an  extent  equal  to  the  diameter  of  the  piston,  must 
be  lifted,  while  there  will  remain  a  vacuum  or  void  space 
below  it  in  the  tube.  If  the  piston  be  only  three  inches  in 
diameter,  it  will  require  the  full  strength  of  a  man  to  draw 
it  to  the  top  of  the  barrel,  and  when  raised,  if  suddenly  let 
go,  it  will  be  forced  back  again  by  the  weight  of  the  air, 
and  will  strike  the  bottom  with  great  violence. 

510.  Supposing  the  surface  of  a  man  to  be  equal  to  14£ 
square  feet,  and  allowing  the  pressure  on  each  square  inch 
to  be  15lbs.,  such  a  man  would  sustain  a  pressure  on  his 
whole  surface  equal  to  nearly  14  tons. 

511.  Now,  that  it  is  the  weight  of  the  atmosphere  which 
presses  the  piston  down,  is  proved  by  the  fact,  that  if  its  di- 
ameter be  enlarged,  a  greater  force,  in  exact  proportion,  will 
be  required  to  raise  it.     And  further,  if  when  the  piston  is 
drawn  to  the  top  of  the  tube,  a  stop-cock,  as  at  fig.  104,  be 
opened,  and  the  air  admitted  under  it,  the  piston  will  not  be 
forced  down  in  the  least,  because  then  the  air  will  press  as 
much  on  the  under,  as  on  the  upper  side  of  the  piston. 

512.  By  accurate  experiments,  an  account  of  which  it  is 
not  necessary  here  to  detail,  it  is  found  that  the  weight  of 
the  atmosphere  on  every  inch  square  of  the  surface  of  the 
earth  is  equal  to  fifteen  pounds.     If,  then,  a  piston  working 
air  tight  in  a  barrel,  be  drawn  up  from  its  bottom,  the  force 
employed,  besides  the  friction,  will  be  just  equal  to  that  re- 
quired to  lift  the  same  piston,  under  ordinary  circumstances, 
with  a  weight  laid  on  it  equal  to  fifteen  pounds  for  every 
square  inch  of  surface. 

513.  The  number  of  square  inches  in  the  surface  of  a 
piston  of  a  foot  in  diameter,  is  113.     This  being  multiplied 
by  the  weight  of  the  air  on  each  inch,  which  being  15 
pounds,  is  equal  to  1695  pounds.     Thus  the  air  constantly 
presses  on  every  surface,  which  is  equal  to  the  dimensions  of 
a  circle  one  foot  in  diameter,  with  a  weight  of  1695  pounds. 

AIR  PUMP. 

514.  The  air  pump  is  an  engine  by  which  the  air  can  be 
pumped  out  of  a  vessel,  or  withdrawn  from  it.     The  vessel 

What  is  the  force  pressing  on  the  piston,  when  drawn  upward,  some- 
times called  ?  How  is  it  proved  that  it  is  the  weight  of  the  atmosphere, 
instead  of  suction,  which  makes  the  piston  rise  with  difficulty'?  What 
is  the  pressure  of  the  atmosphere  on  every  square  inch  of  surface  on 
the  earth  1  What  is  the  number  of  square  inches  in  a  circle  of  one  foot 
in  diameter  1  What  is  the  weight  of  the  atmosphere  on  a  surface  of  a 
foot  in  diameter  1  What  is  the  air  pump  *? 


128 


Alfc  PUMP. 


Fig.  106. 


so  exhausted,  is  called  a  receiver,  and  the  space  thus  left  in 
the  vessel,  after  withdrawing  the  air,  is  called  a  vacuum. 

The  principles  on  which  the  air  pump  is  constructed  are 
readily  understood,  and  are  the  same  in  all  instruments  of 
this  kind,  though  the  form  of  the  instrument  itself  is  often 
considerably  modified. 

515.  The  general   principles  of  its  construction  will  be 
comprehended  by  an  explanation  of  fig.  106.    In  this  figure, 
let  g  be  a  glass  vessel,  or  receiver, 

closed  at  the  top,  and  open  at  the 
bottom,  standing  on  a  perfectly 
smooth  surface,  which  is  called  the 
plate  of  the  air  pump.  Through 
the  plate  is  an  aperture,  a,  which 
communicates  with  the  inside  of 
the  receiver,  and  the  barrel  of  the 
pump.  The  piston  rod,  p,  works 
air  tight  through  the  stuffed  collar, 
c,  and  the  piston  also  moves  air 
tight  through  the  barrel.  At  the 
extremity  of  the  barrel,  there  is  a 
valve  e,  which  opens  outwards,  and 
is  closed  with  a  spring. 

516.  Now  suppose  the  piston  to  be  drawn  up  to  r,  it  will 
then  leave  a  free  communication  between  the  receiver  g, 
through  the  orifice  a,  to  the  pump  barrel  in  which  the  pis- 
ton works.     Then  if  the  piston  be  forced  down  by  its  ban 
die,  it  will  compress  the  air  in  the  barrel  between  d  and  e, 
and,  in  consequence,  the  valve  e  will  be  opened,  and  the  air 
so  condensed  will  be  forced  out.     On  drawing  the  piston  up 
again,  the  valve  will  be  closed,  and  the  external  air  not  be- 
ing permitted  to  enter,  a  vacuum  will  be  formed  in  the  bar- 
rel, from  e  to  a  little  above  d.    When  the  piston  comes  again 
to  c,  the  air  contained  in  the  glass  vessel,  together  with  that 
in  the  passage  between  the  vessel  and  the  pump  barrel,  will 
rush  in  to  fill  the  vacuum.     Thus,  there  will  be  less  air  in 
the  whole  space,  and  consequently  in  -the  receiver,  than  at 
first,  because  all  that  contained  in  the  barrel  is  forced  out  at 
every  stroke  of  the  piston.     On  repeating  the  same  process, 


What  is  the  receiver  of  an  air  pump  1  What  is  a  vacuum  1  In  fig. 
106,  which  is  the  receiver  of  the  air  pump  1  When  the  piston  is  pressed 
down,  what  quantity  of  air  is  thrown  out  1  When  the  piston  is  drawn 
up,  what  is  formed  in  the  barrel  7  How  is  this  vacuum  again  filled 
with  air? 


AIR  PUMP. 


129 


that  is,  drawing  up  and  forcing  down  the  piston,  the  air  at 
each  time  in  the  receiver,  will  become  less  and  less  in  quan- 
tity, and,  in  consequence,  more  and  more  rarefied.  For  it 
must  be  understood,  that  although  the  air  is  exhausted  at 
every  stroke  of  the  pump,  that  which  remains,  by  its  elas- 
ticity, expands,  and  still  occupies  the  whole  space.  The 
quantity  forced  out  at  each  successive  stroke  is  therefore  di- 
minished, until,  at  last,  it  no  longer  has  sufficient  force  be- 
fore the  piston  to  open  the  valve,  when  the  exhausting  pow- 
er of  the  instrument  must  cease  entirely. 

Now,  it  will  be  obvious,  that  as  the  exhausting  power  of 
the  air  pump  depends  on  the  expansion  of  the  air  within  it, 
a  perfect  vacuum  can  never  be  formed  by  its  means,  for  so 
long  as  exhaustion  takes  place,  there  must  be  air  to  be  forced 
out,  and  when  this  becomes  so  rare  as  not  to  force  open  the 
valves,  then  the  process  must  end. 

517.  A  good  air  pump  has  two  similar  pumping  barrels 
to  that  described,  so  that  the  process  of  exhaustion  is  per- 
formed in  half  the  time  that  it  could  be  performed  by  one 
barrel. 

The  barrels,  with  their  Fig  107. 
pistons,  and  the  usual 
mode  of  working  them, 
are  represented  by  fig. 
107.  The  piston  rods  are 
furnished  with  racks,  or 
teeth,  and  are  worked  by 
the  toothed  wheel  a, 
which  is  turned  back- 
wards and  forwards,  by 
the  lever  and  handle  b. 
The  exhaustion  pipe,  c, 
leads  to  the  plate  on 
which  the  receiver 
stands,  as  shown  in  fig. 
107.  The  valves  v,  n,  u, 
and  m,  all  open  upwards. 

518.  To  understand  how  these  pistons  act  to  exhaust  the 
air  from  the  vessel  on  the  plate,  through  the  pipe  c,  we  will 
suppose,  that  as  the  two  pistons  now  stand,  the  handle  b  is 
to  be  turned  towards  the  left.     This  will  raise  the  piston  A, 

Is  the  air  pump  capable  of  producing  a  perfect  vacuum  7  Why  do 
common  air  pumps  have  more  than  one  barrel  and  piston  1  How  are 
the  pistons  of  an  air  pump  worked  ? 


130  CONDENSER. 

while  the  valve  u  will  be  closed  by  the  pressure  of  the  ex- 
ternal air  acting  on  it  in  the  open  barrel  in  which  it  works. 
There  would  then  be  a  vacuum  formed  in  this  barrel,  did 
not  the  valve  m  open,  and  let  in  the  air  coming  from  the  re 
ceiver,  through  the  pipe  c.  When  the  piston,  therefore,  is 
at  the  upper  end  of  the  barrel,  the  space  between  the  piston 
and  the  valve  m,  will  be  filled  with  the  air  from  the  receiver. 
Next,  suppose  the  handle  to  be  moved  to  the  right,  the  pis- 
ton A  will  then  descend,  and  compress  the  air  with  which 
the  barrel  is  filled,  which,  acting  against  the  valve  u,  forces 
it  open,  and  thus  the  air  escapes.  Thus,  it  is  plain,  that 
every  time  the  piston  rises,  a  portion  of  air,  however  rare- 
fied, enters  the  barrel,  and  every  time  that  it  descends,  this» 
portion  escapes,  and  mixes  with  the  external  atmosphere. 

The  action  of  the  other  piston  is  exactly  similar  to  this, 
only  that  B  rises  while  A  falls,  and  so  the  contrary.  It  will 
appear,  on  an  inspection  of  the  figure,  that  the  air  cannot 
pass  from  one  barrel  to  the  other,  for  while  A  is  rising,  and 
the  valve  m  is  open,  the  piston  B  will  be  descending,  so 
that  the  force  of  the  air  in  the  barrel  B,  will  keep  the  valve 
n  closed.  Many  interesting  and  curious  experiments,  illus- 
trating the  expansibility  and  pressure  of  the  atmosphere,  are 
shown  by  this  instrument. 

519.  If  a  withered  apple  be  placed  under  the  receiver, 
and  the  air  is  exhausted,  the  apple  will  swell  and  become 
plump,  in  consequence  of  the  expansion  of  the  air  which  it 
contains  within  the  skin. 

520.  Ether,  placed  in  the  same,  situation,  soon  begins  to 
boil  without  the  influence  of  heat,  because  its  particles,  not 
having  the  pressure  of  the  atmosphere  to  force  them  toge- 
ther, fly  off  with  so  much  rapidity  as  to   produce  ebul- 
lition. 

THE  CONDENSER. 

521.  The  operation  of  the  condenser  is  the  reverse  of  that 
of  the  air  pump,  and  is  a  much  more  simple  machine.    The 
air  pump,  as  we  have  just  seen,  will  deprive  a  vessel  of  its 
ordinary  quantity  of  air.     The  condenser,  on  the  contrary, 

While  the  piston  Ais  ascending,  which  valves  will  be  open,  and 
which  closed  1  When  the  piston  A  descends,  what  becomes  of  the  air 
with  which  its  barrel  was  filled  1  Why  does  not  the  air  pass  from  one 
barrel  to  the  other,  through  the  valves  m  and  n  1  Why  does  an  apple 
placed  in  the  exhausted  receiver  grow  plump  1  Why  does  ether  Boil  in 
the  same  situation  ?  How  does  the  condenser  operate  1 


CONDENSER. 


n'ill  double  or  treble  the  ordinary  quantity  of  air  in  a  close 
vessel,  according  to  the  force  employed. 

This  instrument,  fig.  108,  consists  of  a  pump    Fig.  108. 
barrel  and  piston  a,  a  stop-cock  Z>,  and  the  vessel 
c  furnished. with  a  valve  opening  inwards.    The 
orifice  d  is  to  admit  the  air,  when  the  piston  is 
drawn  up  to  the  top  of  the  barrel. 

522.  To  describe  its  action,  let  the  piston  be 
above  d,  the  orifice  being  open,  and  therefore 
the  instrument  filled  with  air,  of  the  same  den- 
sity as  the   external   atmosphere.      Then,   on 
forcing  the  piston  down,  the  air  in  the  pump 
barrel,  below  the  orifice  d,  will  be  compressed, 
and  will  rush  through  the  stop-cock  b,  into  the 
vessel  c,  where  it  will  be  retained,  because,  on 
again  moving  the  piston  upward,  the  elasticity 
of  the  air  will  close  the  valve  through  which  it 
was  forced.      On  drawing  the  piston  up  again, 
another  portion  of  air  will  rush  in  at  the  orifice 

d,  and  on  forcing  it  down,  this  will  also  be  driven  into  the 
vessel  c;  and  this  process  may  be  continued  as  long  as 
sufficient  force  is  applied  to  move  the  piston,  or  there  is  suf- 
ficient strength  in  the  vessel  to  retain  the  air.  When  the 
condensation  is  finished,  the  stop-cock  b  may  be  turned,  to 
render  the  confinement  of  the  air  more  secure. 

523.  The  magazines  of  air  guns  are  filled  in  the  man- 
ner above  described.     The  air  gun  is  shaped  like  other 
guns,  but  instead  of  the  force  of  powder,  that  of  air  is  em- 
ployed to  project  the  bullet.     For  this  purpose,  a  strong 
hollow  ball  of  copper,  with  a  valve  on  the  inside,  is  screw- 
ed to  a  condenser,  and  the  air  is  condensed  in  it,  thirty  or 
forty  times.     This  ball  or  magazine  is  then  taken  from  the 
condenser,  and  screwed  to  the  gun,  under  the  lock.     By 
means  of  the  lock,  a  communication  is  opened  between  the 
magazine,   and  the  inside  of  the  gun-barrel,  on  which  the 
spring  of  the  confined  air  against  the  leaden  bullet  is  such, 
as  to  throw  it  with  nearly  the  same  force  as  gunpowder. 


Explain  fig.  108,  and  show  in  what  manner  the  air  is  condensed 
Explain  the  principle  of  the  air  gun. 


132 


BAROMETER. 


BAROMETER. 


Fig.  109. 


524.  Suppose  a,  fig.  109,  to  be  a  long  tube, 
with  the  piston  b  so  nicely  fitted  to  its  inside, 
is  to  work  air  tight.     If  the  lower  end  of  the 
lube  be  dipped  into  water,  and  the  piston  drawn 
up  by  pulling  at  the  handle  c,  the  water  will 
follow  the  piston  so  closely,  as  to  be  in  contact 
with  its  surface,  and  apparently  to  be  drawn  up 
by  the  piston,  as  though  the  whole  was  one 
solid  body.     If  the  tube  be  thirty-five  feet  long, 
the  water  will  continue  to  follow  the  piston, 
until  it  comes  to  the  height  of  about  thirty- 
three  feet,  where  it  will  stop,  and  if  the  piston 
be  drawn  up  still  farther,  the  water  will  not 
follow  it,  but  will  remain  stationary,  the  space 
from  this  height,  between  the  piston  and  the 
water,  being  left  a  void  space,  or  vacuum. 

525.  The  rising  of  the  water  in  the  above 
case,  which  only  involves    he  principle  of  the 
common   pump,    is   thought   by   some   to   be  ?-?jS 
caused  by  suction,  the  piston  sucking  up  the   "Y 
water  as  it  is  drawn  upward.     But  according 

to  the  common  notion  attached  to  this  term,  there  is  no  rea- 
son why  the  water  should  not  continue  to  rise  above  the 
thirty-three  feet,  or  why  the  power  of  suction  should  cease 
at  that  point,  rather  than  at  any  other.  Without  entering 
into  any  discussion  on  the  absurd  notions  concerning  the 
power  of  suction,  it  is  sufficient  here  to  state,  that  it  has  long 
since  been  proved,  that  the  elevation  of  the  water,  in  the 
case  above  described,  depends  entirely  on  the  weight  and 
pressure  of  the  atmosphere,  on  that  portion  of  the  fluid 
which  is  on  the  outside  of  the  tube.  Hence,  when  the  pis- 
ton is  drawn  up,  under  circumstances  where  the  air  cannot 
act  on  the  water  around  the  tube,  or  pump  barrel,  no  eleva- 
tion of  the  fluid  will  follow.  This  will  be  obvious,  by  the 
following  experiment. 

Suppose  the  tube,  fig.  109,  to  stand  with  its  lower  end  in  the  water, 
and  the  piston  a  to  be  drawn  upward  thirty-five  feet,  how  far  will  the 
water  follow  the  piston  1  What  will  remain  in  the  tube  between  the 
piston  and  the  water,  after  the  piston  rises  higher  than  thirty-three 
feet  7  What  is  commonly  supposed  to  make  the  water  rise  in  such 
cases'?  Is  there  any  reason  why  the  suction  should  cease  at  33  feet"? 
What  is  the  true  cause  of  the  elevation  of  the  water,  when  the  piston, 
fig.  109,  is  drawn  up  7 


BAROMETER, 


133 


526.  Suppose  fig-.    110  to  be  the  sections,  or    Fig.  110. 
halves,  of  two  tubes,  one  within  the  other,  the  — 
outer  one  being  made  entirely  close,  so  as  to  ad- 
mit no  air,  and  the  space  between  the  two  being 

also  made  air  tight  at  the  top.  Suppose,  also,  that 
the  inner  tube  being  left  open  at  the  lower  end, 
does  not  reach  the  bottom  of  the  outer  tube,  and  c 
thus  that  an  open  space  be  left  between  the  two 
tubes  every  where,  except  at  their  upper  ends, 
where  they  are  fastened  together ;  and  suppose 
that  there  is  a  valve  in  the  piston,  opening  up- 
wards, so  as  to  let  the  air -which  it  contains  es- 
cape, but  which  will  close  on  drawing  the  piston 
upwards.  Now,  let  the  piston  be  at  a,  and  in 
this  state  pour  water  through  the  stop-cock,  c,  un- 
til the  inner  tube  is  filled  up  by  the  piston,  and  the 
space  between  the  two  tubes  filled  up  to  the  same 
point,  and  then  let  the  stop-cock  be  closed.  If 
now  the  piston  be  drawn  up  to  the  top  of  the 
tube,  the  water  will  not  follow  it,  as  in  the  case 
first  described  ;  it  will  only  rise  a  few  inches,  in 
consequence  of  the  elasticity  of  the  air  above  the 
water,  between  the  tubes,  and  in  the  space  above 
the  water,  there  will  be  formed  a  vacuum  be- 
tween the  water  and  the  piston,  in  the  inner  tube. 

527.  The  reason  why  the  result  of  this  experiment  dif- 
fers from  that  before  described,  is,  that  the  outer  tube  pre- 
vents the  pressure  of  the  atmosphere  from  forcing  the  water 
up  the  inner  tube  as  the  piston  rises.     This  may  be  instantly 
proved,  by  opening  the  stop-cock  c,  and  permitting  the  air 
to  press  upon  the  water,  when  it  will  be  found,  that  as  the 
air  rushes  in,  the  water  will  rise  and  fill  the  vacuum,  up  to 
the  piston. 

For  the  same  reason,  if  a  common  pump  be  placed  in  a 
cistern  of  water,  and  the  water  is  frozen  over  on  its  surface, 
so  that  no  air  can  press  upon  the  fluid,  the  piston  of  the 
pump  might  be  worked  in  vain,  for  the  water  would  not,  as 
usual,  obey  its  motion. 

528.  It  follows,  as  a  certain  conclusion  from  such  experi- 

How  is  it  shown  by  fig.  110,  that  it  is  the  pressure  of  the  atmos- 
phere which  causes  the  water  to  rise  in  the  pump  barrel  1  Suppose  the 
jce  prevents  the  atmosphere  from  pressing  on  the  water  in  a  vessel,  can 
the  water  be  pumped  out  1  What  conclusion  follows  from  the  experi- 
ments above  described  1 
12 


134 


BAROMETER. 


ments,  that  when  the  lower  end  of  a  tube  is  placed  in  wnter, 
and  the  air  from  within  removed  by  drawing  up  the  piston, 
that  it  is  the  pressure  of  the  atmosphere  on  the  water  around 
the  tube,  which  forces  the  fluid  up  to  fill  the  space  thus  left 
by  the  air.  It  is  also  proved,  that  the  weight,  or  pressure 
of  the  atmosphere,  is  equal  to  the  weight  of  a  perpendicular 
column  of  water  33  feet  high,  for  it  is  found  (fig.  109)  that 
the  pressure  of  the  atmosphere  will  not  raise  the  water 
more  than  33  feet,  though  a  perfect  vacuum  be  formed  to 
any  height  above  this  point.  Experiments  on  other  fluids, 
prove  that  this  is  the  weight  of  the  atmosphere,  for  if  the 
end  of  a  tube  be  dipped  in  any  fluid,  and  the  air  be  removed 
from  the  tube,  above  the  fluid,  it  will  rise  to  a  greater  or  less 
height  than  water,  in  proportion  as  its  specific  gravity  is 
less  or  greater  than  that  of  water. 

529.  Mercury,  or  quicksilver,  has  a  specific  gravity  of 
about  13^  times  greater  than  that  of  water,  and  mercury  is 
found  to  rise  about  29  inches  in  a  tube  under  the  same  circum- 
stances that  water  rises  33  feet.    Now,  33  feet  is  396  inches, 
which  being  divided  by  29,  gives  nearly  13£,  so  that  mer- 
cury being  13^  times  heavier  than  water,  the  water  will  rise 
under  the  same  pressure  13|  times  higher  than  the  mercury. 

530.  Construction  of  the  Barometer. — The  barometer  is 
constructed  on  the  principle  of  atmospheric        Fig.  111. 
pressure,  which  we  have  thus  endeavoured 

to  explain  and  illustrate  to  common  compre- 
hension. This  term  is  compounded  of  two 
Greek  words,  baros,  weight,  and  metron, 
measure,  the  instrument  being  designed  to 
measure  the  weight  of  the  atmosphere. 

Its  construction  is  simple,  and  easily 
understood,  being  merely  a  tube  of  glass, 
nearly  filled  with  mercury,  with  its  lower 
end  placed  in  a  dish  of  the  same  fluid,  and 
the  upper  end  furnished  with  a  scale,  to 
measure  the  height  of  the  mercury. 

531.  Let  a,  fig.  Ill,  be  such  a  tube,  34  or  fo 
35  inches  long,  closed  at  one  end,  and  open 

at  the  other.    To  fill  the  tube,  set  it  upright, 

How  is  it  proved,  that  the  pressure  of  the  atmosphere  is  equa»  to 
the  weight  of  a  column  of  water,  33  feet  high  7  How  do  experimewts 
on  other  fluids  show  that  the  pressure  of  the  atmosphere  is  equal  to  »he 
weight  of  a  column  of  water,  33  feet  high  7  How  high  does  mercnry 
rise  in  an  exhausted  tube  7  What  is  the  principle  oh  which  the  ba- 
rometer is  constructed  7  What  does  the  barometer  measure  7  Describe 
the  construction  of  the  barometer,  ab  repre^nrid  bv  fig.  111. 


BAROMETER.  135 

and  pour  the  mercury  in  at  the  open  end,  and  when  it  is  en- 
tirely full,  place  the  fore  finger  forcibly  on  this  end,  arid 
then  plunge  the  tube  and  finger  under  the  surface  of  the 
mercury,  before  prepared  in  the  cup  b.  Then  withdraw  the 
finger,  taking  care  that  in  doing  this,  the  end  of  the  tube  is 
not  raised  above  the  mercury  in  the  cup.  When  the  finger 
is  removed,  the  mercury  will  descend  four  or  five  inches, 
and  after  several  vibrations,  up  and  down,  will  rest  at  an 
elevation  of  29  or  30  inches  above  the  surface  of  that  in  the 
cup,  as  at  c.  Having  fixed  a  scale  to  the  upper  part  of  the 
tube,  to  indicate  the  rise  and  fall  of  the  mercury,  the  ba- 
rometer would  be  finished,  if  intended  to  remain  stationary. 
It  is  usual,  however,  to  have  the  tube  enclosed  in  a  mahoga- 
ny or  brass  case,  to  prevent  its  breaking,  and  to  have  the  cup 
closed  on  the  top,  and  fastened  to  the  tube,  so  that  it  can  be 
transported  without  danger  of  spilling  the  mercury. 

532.  The  cup  of  the  portable  barometer  also  differs  from 
that  described,  for  were  the  mercury  enclosed  on  all  sides, 
in  a  cup  of  wood,  or  brass,  the  air  would  be  prevented  from 
acting  upon  it,  and  therefore  the  instrument  would  be  use- 
less.    To  remedy  this  defect,  and  still  have  the  mercury 
perfectly  enclosed,  the  bottom  of  the  cup  is  made  of  leather, 
which,  being  elastic,  the  pressure  of  the  atmosphere  acts 
upon  the  mercury  in  the  same  manner  as  though  it  was  not 
enclosed  at  all.     Below  the  leather  bottom,  there  is  a  round 
plate  of  metal,  an  inch  in  diameter,  which  is  fixed  on  the 
top  of  a  screw,  so  that  when  the  instrument  is  to  be  trans- 
ported,  by  elevating  this  piece  of  metal,  the  mercury  is 
thrown  up  to  the  top  of  the  tube,  and  thus  kept  from  playing 
backwards  and  forwards,  when  the  barometer  is  in  motion. 

533.  A  person  not  acquainted  with  the  principle  of  the 
instrument,  on  seeing  the  tube  turned  bottom  upwards,  will 
be  perplexed  to  understand  why  the  mercury  does  not  fol- 
low the  common  law  of  gravity,  and  descend  into  the  cup  j 
were  the  tube  of  glass  33  feet  high,  and  filled  with  water, 
the  lower  end  being  dipped  into  a  tumbler  of  the  same  fluid, 
the  wonder  would  be  still  greater.     But  as  philosophical 
facts,  one  is  no  more  wonderful  than  the  other,  and  both  are 
readily  explained  by  the  principles  above  illustrated. 

How  is  the  cup  of  the  portable  barometer  made,  so  as  to  retain  the 
mercury,  and  still  allow  the  air  to  press  upon  it  1  What  is  the  use  of  the 
metallic  plate  and  screw,  under  the  bottom  of  the  cup  1  Explain  the  rea- 
«n>n  why  the  mercury  does  not  fall  out  of  the  barometer  tube,  when  its 
open  end  is  downwards. 


136  BAROMETER. 

534.  It  has  already  been  shown,  (528,)  that  it  is  the 
pressure  of  the  atmosphere  on  the  fluid  around  the  tube,  by 
which  the  fluid  within  it  is  forced  upward,  when  the  pump 
is  exhausted  of  its  air.     The  pressure  of  the  air,  we  have 
also  seen,  is  equal  to  a  column  of  water  33  feet  high,  or  of 
a  column  of  mercury  29  inches  high.    Suppose,  then,  a  tube 
33  feet  high  is  filled  with  water,  the  air  would  then  be  en- 
tirely excluded,  and  were  one  of  its  ends  closed,  and  the 
other  end  dipped  in  water,  the  effect  would  be  the  same  as 
though  both  ends  were  closed,  for  the  water  would  not  escape, 
unless  the  air  were  permitted  to  rush  in  and  fill  up  its  place. 
The  upper  end  being  closed,  the  air  could  gain  no  access  in 
that  direction,  and  the  open  end  being  under  water,  is  equal- 
ly secure.     The  quantity  of  water  in  which  the  end  of  the 
tube  is  placed,  is  not  essential,  since  the  pressure  of  a  col- 
umn of  water,  an  inch  in  diameter,  provided  it  be  33  feet 
high,  is  just  equal  to  a  column  of  air  of  an  inch  in  diameter, 
of  the  whole  height  of  the  atmosphere.     Hence  the  water 
on  the  outside  of  the  tube  serves  merely  to  guard  against 
the  entrance  of  the  external  air. 

535.  The  same  happens  to  the  barometer  tube,  when  fill- 
ed with  mercury.     The  mercury,  in  the  first  place,  fills  the 
tube  perfectly,  and  therefore  entirely  excludes  the  air,  so 
that  when  it  is  inverted  in  the  cup,  all  the  space  above  29 
inches  is  left  a  vacuum.     The  same  effect  precisely  would 
be  produced,  were  the  tube  exhausted  of  its  air,  and  the 
open  end  placed  in  the  cup ;  the  mercury  would  run  up  the 
tube  29  inches,  and  then  stop,  all  above  that  point  being  left 
a  vacuum. 

The  mercury,  therefore,  is  prevented  from  falling  out  of 
the  tube,  by  the  pressure  of  the  atmosphere  on  that  which 
remains  in  the  cup ;  for  if  this  be  removed,  the  air  will  enter, 
while  the  mercury  will  instantly  begin  to  descend. 

536.  In  the  barometer  described,  the  rise  and  fall  of  the 
mercury  is  indicated  by  a  scale  of  inches,  and  tenths  of 
inches,  fixed  behind  the  tube ;  but  it  has  been  found,  that 
very  slight  variations  in  the  density  of  ,the  atmosphere,  are 
not  readily  perceived  by  this  method.     It  being,  however, 
desirable  that  these  minute  changes  should  be  rendered  more 
obvious,  a  contrivance  for  increasing  the  scale,  called  the 
wheel  barometer,  was  invented. 

What  fills  the  space  above  29  inches,  in  the  barometer  tubel  In  the 
common  barometer,  how  is  the  rise  and  fall  of  the  mercury  indicated  7 
Why  was  the  wheel  barometer  invented  1 


BAROMETER. 


137 


537.  The  whole  length  of  the  tube  of  the      Fig.  112. 
wheel  barometer,  fig.  112,  from  c  to  a,  is  34 

or  35  inches,  and  it  is  filled  with  mercury,  as 
usual.  The  mercury  rises  in  the  short  leg  to 
the  point  o,  where  there  is  a  small  piece  of 
glass  floating  on  its  surface,  to  which  there  is 
attached  a  silk  string,  passing  over  the  pulley 
p.  To  the  axis  of  the  pulley  is  fixed  an  index, 
or  hand,  and  behind  this  is  a  graduated  circle, 
as  seen  in  the  figure.  It  is  obvious,  that  a  very 
slight  variation  in  the  height  of  the  mercury 
at  0,  will  be  indicated  by  a  considerable  mo- 
tion of  the  index,  and  thus  changes  in  the 
weight  of  the  atmosphere,  hardly  perceptible 
by  the  common  barometer,  will  become  quite 
apparent  by  this. 

538.  The   mercury  in  the  barometer  tube 
being  sustained  by  the  pressure  of  the  atmo- 
sphere, and  its  medium  altitude  at  the  surface 

of  the  earth  being  about  29  inches,  it  might  be  expected 
that  if  the  instrument  was  carried  to  a  height  from  the  earth's 
surface,  the  mercury  would  suffer  a  proportionate  fall,  be- 
cause the  pressure  must  be  less  at  a  distance  from  the  earth, 
than  at  its  surface,  and  experiment  proves  this  to  be  the 
case.  When,  therefore,  this  instrument  is  elevated  to  any 
considerable  height,  the  descent  of  the  mercury  becomes 
perceptible.  Even  when  it  is  carried  to  the  top  of  a  hill, 
or  high  tower,  there  is  a  sensible  depression  of  the  fluid,  so 
that  the  barometer  is  employed  to  measure  the  height  of 
mountains,  and  the  elevation  to  which  balloons  ascend  from 
the  surface  of  the  earth.  On  the  top  of  Mont  Blanc,  which 
is  about  16,000  feet  above  the  level  of  the  sea,  the  medium 
elevation  of  the  mercury  in  the  tube  is  only  14  inches,  while 
on  the  surface  of  the  earth,  as  above  stated,  it  is  29  inches. 

539.  The  medium  range  of  the  barometer  in  several 
countries,  has  generally  been  stated  to  be  about  29  inches. 
It  appears,  however,  from  observations  made  at  Cambridge, 


Explain  fig.  106,  and  describe  the  construction  of  the  wheel  barome- 
ter. What  is  stated  to  be  the  medium  range  of  the  barometer  at  the 
surface  of  the  earth  1  Suppose  the  instrument  is  elevated  from  the 
earth,  what  is  the  effect  on  the  mercury  ?  How  does  the  barometer  in- 
dicate the  heights  of  mountains  1  What  is  the  medium  range  of  the 
mercury  on  Mont  Blanc  1  What  is  stated  to  be  the  medium  range  of 
the  barometer  at  Cambridge] 
12* 


138  BAROMETER. 

in  Massachusetts,  for  the  term  of  22  years,  that  its  range 
there  was  nearly  30  inches. 

540.  Use  of  the  Barometer. — While  the  barometer  stands 
in  the  same  place,  near  the  level  of  the  sea,  the  mercury 
seldom  or  never  falls  below  28  inches,  or   rises  above  31 
inches,  its  whole  range,  while  stationary,  being-  only  about 
3  inches. 

These  changes  in  the  weight  of  the  atmosphere,  indicate 
corresponding  changes  in  the  weather,  for  it  is  found,  by 
watching  these  variations  in  the  height  of  the  mercury,  that 
when  it  falls,  cloudy  or  falling  weather  ensues,  and  that 
when  it  rises,  fine  clear  weather  may  be  expected.  During 
the  time  when  the  weather  is  damp  and  lowering,  and  tho 
smoke  of  chimneys  descends  towards  the  ground,  the  mer- 
cury remains  depressed,  indicating  that  the  weight  oi  the 
atmosphere,  during  such  weather,  is  less  than  it  is  when  the 
sky  is  clear.  This  contradicts  the  common  opinion,  that 
the  air  is  the  heaviest,  when  it  contains  the  greatest  quantity 
of  fog  and  smoke,  and  that  it  is  the  uncommon  weight  of  the 
atmosphere  which  presses  these  vapours  towards  the  ground. 
A  little  consideration  will  show,  that  in  this  case  the  popular 
belief  is  erroneous,  for  not  only  the  barometer,  but  all  the 
experiments  we  have  detailed  on  the  subject  of  specific  grav- 
ity, tend  to  show  that  the  lighter  any  fluid  is,  the  deeper  any 
substance  of  a  given  weight  will  sink  in  it.  Common  ob- 
servation ought^therefore,  to  correct  the  error,  for  every- 
body knows  that  a  heavy  body  will  sink  in  water  while  a 
light  one  will  swim,  and  by  the  same  kind  of  reasoning 
ought  to  consider,  that  the  particles  of  vapour  would  de- 
scend through  a  light  atmosphere,  while  they  would  be 
pressed  up  into  the  higher  regions,  by  a  heavier  air. 

541.  The  principal  use  of  the  barometer  is  on  board  of 
.ships,  where  it  is  employed   to  indicate  the  approach  of 
storms,  and  thus  to  give  an  opportunity  of  preparing  accord- 
ingly ;  and  it  is  found  that  the  mercury  suffers  a  most  re- 
markable depression  before  the  approach  of  violent  winds, 
or  hurricanes.     The  watchful  captain,  particularly  in  south- 
ern latitudes,  is  always  attentive  to  this1  monitor,  and  when 

How  many  inches  does  a  fixed  barometer  vary  in  height  7  When 
the  mercury  falls,  what  kind  of  weather  is  indicated  1  When  the  mer- 
cury rises,  what  kind  of  weather  may  be  expected  1  When  fog  and 
smoke  descend  towards  the  ground,  is  it  a  sign  of  a  light  or  heavy  at- 
mosphere 7  By  what  analogy  is  it  shown  that  the  air  is  lightest  when 
filled  with  vapour  1  Of  what  use  is  the  barometer,  on  board  of  ships  1 
When  does  the  mercury  suffer  the  most  remarkable  depre?sion  1 


PUMP.  139 


he  observes  the  mercury  to  sink  suddenly,  takes  his  meas- 
ures without  delay  to  meet  the  tempest.  During  a  vioient 
storm,  we  have  seen  the  wheel  barometer  sink  a  hundred 
degrees  in  a  few  hours.  But  we  cannot  illustrate  the  use 
of  this  instrument  at  sea  better  than  to  give  the  following 
extract  from  Dr.  Arnot,  who  was  himself  present  at  the  time. 
"  It  was,"  he  says,  "  in  a  southern  latitude.  The  sun  had  just 
set  with  a  placid  appearance,  closing  a  beautiful  afternoon, 
and  the  usual  mirth  of  the  evening  watch  proceeded,  when 
the  captain's  orders  came  to  prepare  with  all  haste  for  a 
storm.  The  barometer  had  begun  to  fall  with  appalling 
rapidity.  As  yet,  the  oldest  sailors  had  not  perceived  even 
a  threatening  in  the  sky,  and  were  surprised  at  the  extent 
and  hurry  of  the  preparations  ;  but  the  required  measures 
were  not  completed,  when  a  more  awful  hurricane  burst 
upon  them,  than  the  most  experienced  had  ever  braved. 
Nothing  could  withstand  it;  the  sails,  already  furled,  and 
closely  bound  to  the  yards,  were  riven  into  tatters ;  even  the 
oare  yards  and  masts  were  in  a  great  measure  disabled  ;  and 
at  one  time  the  whole  rigging  had  nearly  fallen  by  the 
board.  Such,  for  a  few  hours,  was  the  mingled  roar  of  the 
hurricane  above,  of  the  waves  around,  and  the  incessant 
peals  of  thunder,  that  no  human  voice  could  be  heard,  and 
amidst  the  general  consternation,  even  the  trumpet  sounded 
in  vain.  On  that  awful  night,  but  for  a  little  tube  of  mer- 
cury, which  had  given  the  warning,  neither  the  strength  of 
the  noble  ship,  nor  the  skill  and  energies  of  her  commander, 
could  have  saved  one  man  to  tell  the  tale." 

PUMPS. 

542.  There  is  a  philosophical  experiment,  of  which  no 
one  in  this  country  is  ignorant.     If  one  end  of  a  straw  be 
introduced  into  a  barrel  of  cider,  and  the  other  end  sucked 
with  the  mouth,  the  cider  will  rise  up  through  the  straw, 
and  may  be  swallowed. 

The  principles  which  this  experiment  involve,  are  exactly 
the  same  as  those  concerned  in  raising  water  by  the  pump. 
The  barrel  of  cider  answers  to  the  well,  the  straw  to  the 
pump  log,  and  the  mouth  acts  as  the  piston,  by  which  the 
air  is  removed. 

543.  The  efficacy  of  the  common  pump,  in  raising  water, 

What  remarkable  instance  is  stated,  where  a  ship  seemed  to  be  saved 
l>y  the  use  of  the  barometer  1  What  experiment  is  stated,  as  Ulustra- 
ling  the  principle  of  the  common  pump  1 


140 


PUMP. 


Fig.  113. 


depends  upon  the  principle  of  atmospheric  pressure,  wL«:h 
has  been  fully  illustrated  under  the  articles  air  pump  and 
barometer. 

544.  These  machines  are  of  three   kinds,  namely,  the 
sucking,  common  pump,  the  lifting  pump,  and  the  forcing 
pump. 

Of  these,  the  common  or  household 
pump  is  the  most  in  use,  and  for  ordi- 
nary purposes,  the  most  convenient.  It 
consists  of'B  long  tube,  or  barrel,  called 
the  pump  log,  which  reaches  from  a 
few  feet  above  the  ground  to  near  the 
bottom  of  the  well.  At  a,  fig.  113,  is  a 
valve,  opening  upwards,  called  the  pump 
box.  When  the  pump  is  not  in  action, 
this  is  always  shut.  The  piston  b,  has 
an  aperture  through  it,  which  is  closed 
by  a  valve,  also  opening  upwards. 

By  the  pupil  who  has  learned  what 
has  been  explained  under  the  articles  air 
pump,  and  barometer,  the  action  of  this 
machine  will  be  readily  understood. 

545.  Suppose  the  piston  b  to  be  down 

to  a,  then  on  depressing  the  lever  c,  a  vacuum  would  be 
formed  between  a  and  b,  did  not  the  water  in  the  well  rise, 
in  consequence  of  the  pressure  of  the  atmosphere  on  that 
around  the  pump  log  in  the  well,  and  take  the  place  of  the 
air  thus  removed.  Then,  on  raising  the  end  of  the  lever, 
the  valve  a  closes,  because  the  water  is  forced  upon  it,  in 
consequence  of  the  descent  of  the  piston,  and  at  the  same 
time  the  valve  in  the  piston  b  opens,  and  the  water,  which 
cannot  descend,  now  passes  above  the  valve  b.  Next,  on 
raising  the  piston,  by  again  depressing  the  lever,  this  por- 
tion of  water  is  lifted  up  to  b,  or  a  little  above  it,  while  an- 
other portion  rushes  through  the  valve  a  to  fill  its  place- 
After  a  few  strokes  of  the  lever,  the  space  from  the  piston  b 
to  the  spout,  is  filled  with  the  water,  where,  on  continuing 
to  work  the  lever,  it  is  discharged  in  a  constant  stream. 


On  what  does  the  action  of  the  common  pump  depend  7  How  many 
kinds  of  pumps  are  mentioned  1  Which  kind  is  the  common  1  Describe 
the  common  pump.  Explain  how  the  common  pump  acts.  When  the 
lever  is  depressed,  what  takes  place  in  the  pump  barrel  7  When  the 
lever  is  elevated,  what  takes  place  1  How  far  is  the  water  raised  by  at- 
mospheric pressure,  and  now  far  by  lifting  ? 


PUMP. 


141 


Although,  in  common  language,  this  is  called  the  suction 
pump,  still  it  will  be  observed,  that  the  water  is  elevated  by 
suction,  or,  in  more  philosophical  terms,  by  atmospheric 
pressure,  only  above  the  valve  a,  after  which  it  is  raised  by 
lifting  up  to  the  spout.  The  water,  therefore,  is  pressed 
into  the  pump  barrel  by  the  atmosphere,  and  thrown  out  by 
lifting. 

546.  The  lifting  pump,  properly  so  called,  has  the  piston 
in  the  lower  end  of  the  barrel,  and  raises  the  water  through 
the  whole  distance,  by  forcing  it  upward,  without  the  agency 
of  the  atmosphere. 

547.  In  the  suction  pump,  the  pressure  of  the  atmosphere 
will  raise  the  water  33  or  34  feet,  and  no  more,  after  which 
it  may  be  lifted  to  any  height  required. 

548.  The  forcing  pump  differs  from  both  these,  in  hav- 
ing its  piston  solid,  or  without  a  valve,  and  also  in  having  a 
side  pipe,  through  which  the  water  is  forced,  instead  of 
rising  in  a  perpendicular  direction,  as  in  the  others. 


549.  The  forcing  pump  is 
represented  by  fig.  114,  where 
a  is  a  solid  piston,  working  air 
tight  in  its  barrel.     The  tube  c 
leads  from  the  barrel  of  the 
air  vessel  d.   Through  the  pipe 
p,  the  water  is  thrown  into  the 
open   air.     g  is  a  gauge,  by 
which  the  pressure  of  the  water 
in  the  air  vessel  is  ascertained. 
Through  the  pipe  i,  the  water 
ascends  into  the  barrel,  its  up-  * 
per  end  being  furnished  with 

a  valve  opening  upwards. 

550.  To  explain  the  action 
of  this  pump,  suppose  the  pis- 
ton to  be  down  to  the  bottom 
of  the  barrel,  and  then  to  be 
raised  upward  by  the  lever  I ; 
the  tendency  to  form  a  vacuum 
in  the  barrel,  will  bring  the 
water  up  through  the  pipe  i, 


Fig.  114. 


How  does  the  lifting  pump  differ  from  the  common  pump  ?  How 
does  the  forcing  pump  differ  from  the  common  pump*  Explain  fig. 
114,  and  show  in  what  manner  the  water  is  brought  up  through  the 
pipe  i,  and  afterwards  thrown  out  at  the  pipe  p. 


142  FIRE  ENGINE. 

by  the  pressure  of  the  atmosphere.  Then,  on  depressing 
the  piston,  the  valve  at  the  bottom  of  the  barrel  will  be 
closed,  and  the  water,  not  finding  admittance  through  the 
pipe  whence  it  came,  will  be  forced  through  the  pipe  c,  and 
opening  the  valve  at  its  upper  end,  will  enter  into  the  air 
vessel  d,  and  be  discharged  through  the  pipe  p,  into  the 
open  air. 

,  The  water  is  therefore  elevated  to  the  piston  barrel  by 
the  pressure  of  the  atmosphere,  and  afterwards  thrown  out 
by  the  force  of  the  piston.  It  is  obvious,  that  by  this  ar- 
rangement, the  height  to  which  this  fluid  may  be  thrown, 
will  depend  on  the  power  applied  to  the  lever,  and  the 
strength  with  which  the  pump  is  made. 

The  air  vessel  d  contains  air  in  its  upper  part  only,  the 
lower  part,  as  we  have  already  seen,  being  filled  with  water. 
The  pipe  p,  called  the  discharging  pipe,  passes  down  into 
the  water,  so  that  the  air  cannot  escape.  The  air  is  there- 
fore compressed,  as  the  water  is  forced  into  the  lower  part 
of  the  vessel,  and  re-acting  upon  the  fluid  by  its  elasticity, 
throws  it  out  of  the  pipe  in  a  continued  stream.  The  con- 
stant stream  which  is  emitted  from  the  direction  pipe  of  the 
fire  engine,  is  entirely  owing  to  the  compression  and  elas- 
ticity of  the  air  in  its  air  vessel.  In  pumps,  without  such  a 
vessel,  as  the  water  is  forced  upwards,  only  while  the  piston 
is  acting  upon  it,  there  must  be  an  interruption  of  the  stream 
while  the  piston  is  ascending,  as  in  the  common  pump. 
The  air  vessel  is  a  remedy  for  this  defect,  and  is  found  also 
to  render  the  labour  of  drawing  the  water  more  easy,  be- 
cause the  force  with  which  the  air  in  the  vessel  acts  on  the 
water,  is  always  in  addition  to  that  given  by  the  force  of  the 
piston. 

FIRE  ENGINE. 

551.  The  fire  engine  is  a  modification  of  the  forcing 
pump.  It  consists  of  two  such  pumps,  the  pistons  of  which 
are  moved  by  a  lever  with  equal  arms,  the  common  fulcrum 
being  at  c,  fig.  115.  While  the  piston  a  is  descending,  the 

Why  does  not  the  air  escape  from  the  air  vessel  in  this  pump  ? 
What  effect  does  the  air  vessel  have  on  the  stream  discharged  1  Why 
does  the  air  vessel  render  the  labour  of  raising  the  water  more  easy  1 


FIRE  ENGINE. 


143 


Fig.  115. 


other  piston,  b,  is  ascending. 
The  water  is  forced  by  the 
pressure  of  the  atmosphere, 
through  the  common  pipe  p, 
and  then  dividing,  ascends 
into  the  working  barrels  of 
each  piston,  where  the  valves, 
on  both  sides,  prevent  its  re- 
turn. By  the-  alternate  de- 
pression of  the  pistons,  it  is 
then  forced  into  the  air  box  d, 
ind  then  by  the  direction  pipe 
e,  is  thrown  where  it  is  want- 
ed. This  machine  acts  pre- 
cisely like  the  forcing  pump, 
only  that  its  power  is  doubled, 
by  having  two  pistons  instead  of  one. 

552.  There  is  a  beautiful  fountain,  called  the  fountain 
vf  Hiero,  which  acts  by  the  elasticity  of  the  air,  and  on  the 


Fig.  116. 


same  principle  as  that  already  de- 
scribed. Its  construction  will  be 
understood  by  fig.  1 16,  but  its  form 
may  be  varied  according  to  the  dic- 
tates of  fancy  or  taste.  The  boxes 
a  and  b,  together  with  the  two  tubes, 
are  made  air  tight,  arid  strong,  in 
proportion  to  the  height  it  is  desired  d 
the  fountain  should  play. 

553.  To  prepare  the  fountain  for 
action,  fill  the  box  a,  through  the 
spouting  tube,  nearly  full  of  water. 
The  tube  c,  reaching  nearly  to  the 
top  of  the  box,  will  prevent  the  wa- 
tf>r  from  passing  downwards,  while 
the  spouting  pipe  will  prevent  the 
air  from  escaping  upwards,  after  the 
vessel  is  about  half  filled  with  wa- 
ter. Next,  shut  the  stop-cock  of  the 
spouting  pipe,  and  pour  water  into 
the  open  vessel  d.  This  will  descend  into  the  vessel  b, 
through  the  tube  e,  which  nearly  reaches  its  bottom,  so  that 

Explain  fig.  115,  and  describe  the  action  of  the  fire  engine.  What 
causes  the  continued  stream  from  the  direction  pipe  of  this  engine  ? 
How  is  the  fountain  of  Hiero  constructed  1 


L44  STEAM  ENGINE. 

after  a  few  inches  of  water  are  poured  in,  air  can 
escape,  except  by  the  tube  c,  up  into  the  vessel  a,  The  air 
will  then  be  compressed  by  the  weight  of  the  column  of 
water  in  the  tube  e,  and  therefore  the  force  of  the  water 
from  the  jet  pipe  will  be  in  proportion  to  the  height  of 
this  tube.  If  this  tube  is  20  or  30  feet  high,  on  turning  the 
stop-cock,  a  jet  of  water  will  spout  from  the  pipe  that  will 
amuse  and  astonish  those  who  have  never  before  seen  such 
an  experiment. 

STEAM  ENGINE. 

555.  Like  most  other  great  and  useful  inventions,  the 
steam  engine,  from  a  very  simple  contrivance,  for  the  pur- 
pose of'  raising  water,  has  been  improved  at  various  times, 
and  by  a  considerable  number  of  persons,  until  it  has  been 
brought  to  its  present  state  of  power  and  perfection. 

556.  By  most  writers,  the  origin  of  this  invention  is  at- 
tributed to  the  Marquis  of  Worcester,  an  Englishman,  in 
about  1663.    But  as  he  has  left  no  drawing,  nor  such  a  par- 
ticular description  of  his  machine,  as  to  enable  us  to. define 
its  mode  of  action,  it  is  impossible,  at  the  present  time,  to 
say  how  much  credit  ought  to  be  attributed  to  this  invention. 

557.  It  is  certain,  that  the  first  engines  had  neither  cylin- 
ders, piston,  nor  gearing,  by  which  machinery  was  made  to 
revolve,  these  most  important  parts  having  been  added  by 
succeeding  inventors  and  improvers. 

558.  Captain  Savary's  Engine. — The  first  steam  engine 
of  which  we  have  any  definite  description,  was  that  invented 
by  Capt.  Thomas  Savary,  an  Englishman,  in  1698.     By  this 
engine,  the  water  was  raised  to  a  certain-  height,  by  means 
of  a  vacuum  formed  by  the  condensation  of  steam,  and  then 
was  forced  upward  by  the  direct  force  of  steam  from  the 
boiler. 

559.  It  appears  that  the  idea  of  forming  a  vacuum  by  the 
condensation  of  steam,  was  suggested  to   Capt.  Savary  by 
the  following  circumstances  : 

Having  drank  a  flask  of  Florence  wine  at  an  inn,  he 
threw  the  empty  flask  on  the  fire,  and  a  moment  after  called 
for  a  basin  of  water  to  wash  his  hands.  A  small  quantity 
of  the  wine  which  remained  in  the  flask,  began  to  boil,  and 

On  what  will  the  height  of  the  jet  from  Hiero's  fountain  depend  1 
What  was  the  origin  of  the  steam  engine  1  To  whom  is  this  inven 
tion  generally  attributed  1  Who  was  the  inventor  of  the  first  engine  of 
•which  we  have  any  definite  description?  What  was  the  origin  of 
Capt.  Savary's  idea  of  raising  water  by  a  vacuum  1 


STEAM  ENGINE.  145 

steam  issued  from  its  mouth.  Observing  this,  it  occurred  to 
him  to  try  what  effect  would  be  produced  by  inverting  the 
flask,  and  plunging  its  mouth  into  the  cold  water  of  the 
basin.  Putting  on  a  thick  glove  to  defend  his  hand  from 
the  heat,  he  seized  the  flask,  and  the  moment  he  plunged  its 
mouth  into  the  water,  the  liquid  rushed  up,  and  nearly  rilled 
the  vessel. 

560.  Savary  states,  that  this  circumstance  suggested  im- 
mediately to  him  the  possibility  of  giving  effect  to  the  at- 
mospheric pressure,  by  creating  a  vacuum  by  the  condensa- 
tion of  steam.     His  plan  was  to  lift  the  water  from  the 
mines  to  a  certain  height,  in  this  manner,  and  to  force  it  to 
the  elevation  required  by  the  direct  power  of  the  steam. 

561.  Fig.  117  will  show  the  principle,  though  not  the 
precise  form,  of  Savary's  steam  engine.     It  consists  of  a 
boiler,  a,  for  the  generation  Fig- 117. 

of  steam,  which  is  furnished 
with  a  safety  valve,  b,  which 
opens  and  lets  off  the  steam, 
when  the  pressure  would 
otherwise  endanger  the  burst- 
ing of  the  boiler.  From  the 
boiler  there  proceeds  the 
steam  pipe,  furnished  with 
the  stop-cock,  c,  to  the  steam, 
vessel,  d.  From  the  bottom 
of  the  steam  vessel,  there  c 
scends  the  pipe  e,  called  the 
suction  pipe,  which  dips  into 
the  well,  or  reservoir,  from 
which  the  water  is  to  be  rais- 
ed. This  pipe  is  furnished 
with  a  valve,  opening  up- 
wards, at  its  upper  end.  From 
the  upper  end  of  the  steam 
vessel  rises  another  pipe,  /, 
called  the  force  pipe,  which 
also  has  a  valve  opening  up- 
wards. To  this  pipe  is  attached  a  small  cistern,  g,  furnished 
with  a  short  pipe,  called  the  condensing  pipe,  and  from  which 
cold  water  can  be  drawn,  so  as  to  fall  upon  the  steam  vessel  d. 

What  are  the  parts  of  which  Savary's  engine  consisted  1  Describe 
the  process  by  which  water  is  raised  from  the  well  to  the  steam  vessel 
with  this  engine. 

13 


146  STEAM  ENGINE. 

562.  To  trace  the  action  of  this  simple  apparatus,  suppose 
the  steam  vessels  and  tubes  to  be  filled  with  atmospheric  air, 
which  of  course  would  be  the  case,  while  the  whole  remains 
cold.    But  on  making  a  fire  under  the  boiler,  steam  is  gen- 
erated, which,  on  turning  the  stop-cock  c,  is  let  into  the. 
steam  vessel  d,  where  for  a  time  it  is  condensed,  and  falls 
down  in  drops  on  the  sides  of  the  vessel.     The  continued 
supply  of  steam  will,  however,  soon  heat  the  vessel,  so  that 
no  more  vapour  will  be  condensed,  and  its  elastic  force  will 
open  the  upper  valve,  and  it  will  pass  off  through  the  pipe 
/,  while,  at  the  same  time,  and  by  the  same  force,  the  lower 
valve  will  be  closed. 

563.  When  the  steam  has  driven  all  the  atmospheric  air 
from  the  vessel  d,  and  the  upper  pipe,  and  there  remains  no- 
thing in  them  but  the  pure  vapour  of  water,  suppose  the 
stop-cock  c  to  be  turned,  so  as  to  stop  the  further  supply  of 
steam,  and  that  at  the  same  time  cold  water  be  allowed  to 
run  from  the  condensing  cistern  g,  on  the  steam  vessel  d. 
The  steam  will  thus  be  condensed  into  water,  leaving  the 
interior  of  the  vessel  a  vacuum.     The  pressure  of  the  at- 
mosphere will  close  the  upper  valve,  while  the  same  press- 
ure acting  on  the  water  surrounding  the  tube  in  the  well, 
will  force  the  fluid  up  to  take  the  place  of  the  vacuum  in 
the  steam  vessel  d. 

564.  The  height  to  which  water  may  thus  be  elevated, 
we  have  already  seen,  is  about  33  feet,  provided  the  vacuum 
be  perfect,  but  Savary  was  never  able  to  elevate  it  more  than 
26  feet  by  this  method. 

We  now  suppose  that  the  steam  vessel  is  filled  with  wa- 
ter, by  the  creation  of  a  vacuum,  and  the  pressure  of  the  at- 
mosphere alone,  the  direct  force  of  the  steam  having  no 
agency  in  the  process.  But  in  order  to  continue  the  eleva- 
tion above  the  level  of  the  steam  vessel,  the  elastic  pressure 
of  the  steam  must  be  employed. 

565.  Let  us  now  suppose,  therefore,  that  the  vessel  d  is 
nearly  full  of  water,  and  that  the  stop-cock  c  is  turned,  so  as 
to  admit  the  steam  from  the  boiler  through  the  tube  to  the 
upper  part  of  the  steam  vessel,  and  consequently  above  the 
water.     At  first,  the  steam  will  be  condensed  by  the  cold 
surface  of  the  water,  but  as  hot  water  is  lighter  than  cold, 
there  will  soon  become  a  film  of  heated  liquid,  by  the  con- 
How  high  did  Savary's  engine  elevate  water  by  atmospheric  press- 
ure?   Describe  the  manner  in  which  the  water  was  elevated  above  the 
eleam  vessel. 


STEAM  ENGINE.  147 

iensation  of  the  steam  on  the  surface  of  the  cold,  so  that,  in 
a  few  minutes,  no  more  steam  will  be  condensed.  Then  the 
direct  force  of  the  steam  pressing  upon  the  water,  will  drive 
it  through  the  force  pipe/  and  opening  the  valve,  will  de- 
rate it  to  the  height  required. 

566.  When  all  the  water  has  been  driven  out,  the  con- 
tinued influx  of  the  steam  will  heat  the  vessel  until  no  far- 
.her  condensation  will  take  place,  and  the  vessel  will  be  fill- 
ed with  the  pure  vapour  of  water,  as  before,  when  the  steam, 
oeing  shut  off,  and  the  cold  water  let  on,  a  vacuum  will  be 
produced,  and  another  portion  of  water  be  elevated  to  take 
its  place,  as  already  described,  and  so  on  continually. 

This  machine,  though  a  mere  apology  for  the  complex 
and  effective  steam  engines  of  the  present  day,  is  neverthe- 
less highly  creditable  to  the  mechanical  genius  of  the  in- 
ventor, considering  the  low  state  of  science  and  mechanical 
knowledge  at  that  time. 

567.  These  engines  were  chiefly  employed  in  the  drain- 
age of  the  coal  mines,  and  were  sufficiently  powerful  to 
elevate  the  water  to  the  height  of  about  90  feet,  including 
both  the  atmospheric  pressure,  and  the  direct  force  of  the 
steam.     But  the  process  was  exceeding  slow ;  the  quantity 
of  steam  wasted  in  the  process  was  very  great,  and  the  quan- 
tity of  fuel  consumed  immense.      Besides  these  disadvan- 
tages, the  bursting  power  of  the  steam,  when  applied  with 
a  force  sufficient  to  elevate  a  column  of  water  60  feet  high, 
was  such  as  to  require  vessels  of  great  strength,  and,  conse- 
quently, engines  of  small  capacity  only  could  be  employed. 
In  addition  to  these  defects,  where  the  mine  was  several 
hundred  feet  deep,  three  or  four  engines  must  be  employed, 
since  each  could  elevate  the  water  only  about  90  feet.    It  is 
hardly  necessary,  therefore,  to  say,  that  Savary's  engine  did 
not  answer  the  principal  object  of  its  design,  that  of  drain- 
ing the  English  mines. 

568.  Newcomers  Engine.-?-Th&  steam  engine  which  suc- 
ceeded that  of  Savary,  was  invented  by  Thomas  Newcomen, 
a  blacksmith,  of  Dartmouth,  in  England.     Newcomen's  pa- 
tent was  dated  1707,  and  in  it  Capt.  Savary  was  united,  in 
consequence  of  his  discovery  of  the  method  of  forming  a 
vacuum    by  the    condensation  of  steam,   as   already  de- 
scribed. 

What  is  said  of  Savary's  invention  1  What  were  the  chief  objec- 
tions to  Savary's  engines  1  Whose  steam  engine  succeeded  that  of 
Savary  1  At  what  time  was  Ntwcomen's  engine  invented  1 


148 


STEAM  ENGINE 


569.  The  great  object  of  Newcomen's  invention,  like  that 
of  Savary,  was  to  drain  the  English  mines.     To  do  this,  he 
proposed  to  connect  one  arch  head  of  a  working  beam  to  a 
pump  rod,  while  the  other  arch  head  should  be  connected 
with  a  piston  and  rod  moving  in  a  cylinder,  which  piston 
should  be  made  to  descend  by  the  pressure  of  the  atmosphere, 
in  consequence  of  creating  a  vacuum  under  it  by  the  con- 
densation of  steam.     When  the  piston  had  been  made  to  de- 
scend in  this  manner,  by  which  the  pump  at  the  other  end 
of  the  beam  was  to  be  worked,  the  piston  was  again  to  be 
drawn  up  by  the  weight  of  the  pump  rod,  so  that  this  en- 
gine was  moved  alternately  by  means  of  a  vacuum  at  one 
end  of  the  beam,  and  a  weight  at  the  other. 

570.  This  was  the  first  proposition  which  had  been  made 
to  work  a  piston  by  means  of  steam,  or  rather  by  means  of 
a  vacuum,  created  by  the  condensation  of  steam,  and  may  be 
considered  as  the  origin  of  the  present  mode  of  working  all 
steam  engines. 

571.  It  is  proper  to  distinguish  this  as  the  atmospheric 

Fig.  118. 


In  what  manner  was  Newcomen's  engine  worked  ?  What  is  said  of 
the  originality  of  this  invention1?  Why  is  Newcomen's  distinguished 
by  the  name  of  the  atmospheric  engine  1 


STEAM  ENGINE.  149 

engine,  since  its  movement  depended  on  the  pressure  of  the 
atmosphere  alone. 

The  adjoining  cut,  fig.  118,  and  the  following  description, 
will  show  the  plan  and  movement  of  Newcomen's  engine. 

The  boiler  a,  furnished  with  a  safety  valve  on  the  top, 
has  a  steam  pipe,  b,  proceeding  to  the  cylinder  d.  The  pis- 
ton c  is  of  solid  metal,  and  works  air  tight  in  the  cylinder. 
The  piston  is  attached  by  its  rod  to  the  arch  head  of  the 
working  beam  /  To  the  other  arch  head  is  attached 
»he  pump  rod  g,  which  is  connected  with  its  piston  in  the 
pump  k.  This  pump  descends  to  the  water,  to  be  drawn  up 
by  the  action  of  the  engine.  The  small  forcing  pump  h  is 
supplied  with  water  by  the  pump  k,  and  is  designed  to  raise 
a  portion  of  the  fluid  through  the  condensing  pipe  i,  to  the 
cylinder  by  which  the  steam  is  condensed.  This  pump,  as 
well  as  the  other,  is  worked  by  the  action  of  the  working 
beam. 

572.  To  describe  the  action  of  this  engine,  let  us  suppose 
that  the  piston  c  is  drawn  up  to  the  top  of  the  cylinder,  by 
the  weight  of  the  pump  rod  g,  as  represented  in  the  figure; 
that  the  cylinder  itself  is  filled  with  steam,  and  that  the  stop- 
cock of  the  steam  pipe  is  turned  so  that  no  more  steam  is 
admitted.     The  cylinder  was  surrounded  by  another  circu- 
lar vessel,  leaving  a  space  between  the  two,  into  which  the 
cold   water  was  admitted.     Suppose  the  cold  water  to  be 
drawn  by  trie  condensing  pipe  i  into  this  space,  and  conse- 
quently the  steam  to  be  condensed,  leaving  a  vacuum  within 
the  cylinder.     The  consequence  would  be,  that  the  pressure 
of  the  atmosphere  on  the  piston  would  instantly  force  it 
down  to  the  bottom  of  the  cylinder.     This  would  give  ac- 
tion to  the  pump  k,  by  which  a  quantity  of  water  would  be 
drawn  up  from  the  well. 

573.  Now  the  piston  being  forced  to  the  bottom  of  the  cyl- 
inder by  the  pressure  of  the  atmosphere,  unless  relieved 
from  that  pressure,  would  not  rise  again,  and  therefore  a 
quantity  of  steam  must  be  admitted  under  it  by  the  pipe  b, 
so  as  to  balance  the  pressure  on  the  upper  side.    When  this 
is  effected,  the  piston  is  immediately  drawn  again  to  the  top 
of  the  cylinder  by  the  weight  of  the  pump  rod,  and  thus  the 
several  parts  of  the  engine  become  in  the  precise  position 
ihat  they  were  when  our  description  began ;  and  in  order 

Describe  the  several  parts  of  this  engine.  Describe  the  action  of  thU 
tngine. 

13* 


150  STEAM  EKG1NE. 

again  to  depress  the  piston,  a  vacuum  must  once  more  be 
produced  by  the  admission  of  cold  water  on  the  cylinder, 
and  so  on  continually. 

The  power  of  these  engines,  although  operating  by  thr* 
pressure  of  the  atmosphere  alone,  was  much  greater  than 
might  at  first  be  supposed. 

574.  The  pressure  of  the  atmosphere,  when  operating  on  a 
perfect  vacuum,  as  we  have  already  shown,  amounts  to  15 
pounds  on  every  square  inch  of  surface.    The  power  of  this 
engine  therefore  depended  entirely  on  the  number  of  square 
inches  which  the  piston  presented  to  this  pressure. 

575.  Now  the  number  of  square  inches  in  a  circle  may 
be  very  nearly  found  by  the  following  rule  : 

Multiply  the  number  of  inches  in  the  diameter  by  itself: 
divide  the  product  by  14,  and  multiply  the  quotient  thus  ob- 
tained by  11,  and  the  result  will  be  the  number  of  square 
inches  in  the  circle. 

576.  Thus,   a   piston   having  a    diameter   of  only    13 
inches,  would  be  pressed  down  by  a  weight  equal   1980 
pounds,  or  nearly  one  ton ;  and  a  piston  twice  this  diameter, 
or  26  inches,  would  be  acted  upon  by  a  weight  equal  7920 
pounds,  or  nearly  four  tons.    These  estimates  are,  however, 
too  high  for  practical  results,  for,  after  allowing  for  the 
friction  of  the  piston,  and  the  imperfection  of  the  vacuum,  it 
was  found,  in  practice,  that  only  about  1 1  pounds  of  force 
to  the  square  inch  could  actually  be  obtained. 

577.  Soon  after  the  construction  of  these  engines,  an  acci- 
dental circumstance  suggested  to  the  inventor  a  much  better 
method  of  condensation  than  the  effusion  of  cold  water  on 
the  cylinder,  which,  as  we  have  seen,  was  that  first  prac- 
tised.    In  order  to  keep  the  piston  air-tight,  it  was  neces- 
sary to  have  a  quantity  of  water  on  it,  which  was  supplied 
from  a  pipe  placed  over  it.     On  one  occasion,  a  piston  was 
observed  to  descend  several  times  with  unusual  rapidity,  and 
this  without  waiting  for  the  usual  supply  of  condensing 
water.     On   examination,  it  was   found   that   an    aperture 
through  the   piston  admitted  the  cold  water  directly  to  the 
steam  in  the  cylinder,  by  which  it  was  instantly  condensed. 

What  is  said  of  the  power  of  these  engines  1  How  may  the  num- 
ber of  square  inches  in  a  circle  be  found  1  What  would  be  the  amount 
of  pressure  on  a  piston  of  13  inches  in  diameter  1  What  would  be  the 
pressure  on  a  piston  of  26  inches  in  diameter1?  How  much  must  be 
allowed  for  friction  and  imperfection  of  vacuum  1  How  did  Newco- 
men  discover  an  improved  method  of  condensing  steam  1 


STEAM  ENGINE.  151 

578.  On  this  suggestion,  INewcomen  abandoned  his  first 
method,  and  by  the  addition  of  a  pipe,  through  which  a  jet 
of  cold  water  was  thrown  into  the  cylinder,  condensed  the 
steam  instantly,  and  much  more  perfectly  than  could  be  done 
even  by  waiting  a  long  time  for  the  gradual  cooling  of  the 
cylinder  by  the  old  method.     This  was  a  highly  important 
improvement,  and  substantially  is  the  method  practised  to 
this  day. 

579.  Newcomen's  machine,  though  so  imperfect,  when 
compared  with  those  of  the  present  day,  as  hardly  to  deserve 
the  name  of  a  steam  engine,  was  extensively  employed  in 
draining  the  English  mines,  and  for  nearly  half  a  century 
was  the  only  machine  moved  by  the  application  of  steam. 
And  notwithstanding  its  material  and  obvious  imperfections, 
still  it  must  be  considered  as  a  lasting  monument  of  the  com- 
bining and  inventive  powers  of  a  man,  who  appears  origi- 
nally to  have  had  no  advantages  in  life,  above  what  his  ex- 
perience and  observations  as  a  blacksmith  gave  him. 

580.  Watt's  Engine. — It  does  not  appear  that  any  con- 
siderable improvements  were  made  on  Newcomen's  steam 
apparatus,  until  the  time  when  James  Watt  began  his  ex- 
periments and  inventions  in  about  1763. 

Watt  was  born  at  Greenock,  in  Scotland,  and  pursued  the 
business  of  a  mathematical  instrument  maker  in  London. 
He  was  endowed  with  a  mind  of  the  highest  order,  both  as 
a  philosopher  and  inventor,  as  will  be  evinced  by  the  new 
combinations,  improvements,  and  inventions,  which  he  ap- 
plied to  nearly  every  part  of  the  apparatus  to  which  steam 
has  been  employed  as  a  moving  power. 

581.  Some  of  his  first  improvements,  or  perhaps  more 
properly,  inventions,  were  a  pump,  for  the  removal  of  the 
air  and  water,  which  were  accumulated  by  the  condensation 
of  the  steam — the  application  of  melted  wax,  or  tallow,  in- 
stead of  water,  to  lubricate  the  piston,  and  keep  it  air-tight, 
and  the  employment  of  steam  above  the  piston,  to  press  it 
down,  instead  of  the  atmosphere,  as  in  Newcomen's  engine. 

For  the  latter  purpose,  it  was  necessary  to  close  the  top 
of  the  cylinder,  and  allow  the  piston-rod  to  play  through  a 
steam  tight  stuffing-box,  as  is  done  at  the  present  time  in  all 
steam  engines. 

What  is  said  of  Newcomen's  invention  on  the  whole  1  "When  did 
Watt  begin  his  experiments'?  What  is  said  of  Watt's  capacity? 
What  were  among  the  first  improvements  of  the  steam  engine  1  What 
change  must  be  made  in  Newcomen's  cylinder,  in  order  to  press  down 
he  piston  with  steam  1 


152 


STEAM  ENGINE. 


S>*v±i* 


"hj 


f 


582.  This  improvement  is  represented  by  fig.  1 19,  where 
$  is  the  steam  pipe  proceeding  from  the   boiler,  and   oy 
which  steam   is   admitted  to  Fig.  119. 

the  cylinder.  The  piston  h 
works  air-tight  in  the  cylin- 
der g\  the  rod  of  which  passes 
air-tight  through  the  stuffing- 
box  i.  The  upper  valve  box  

a  contains    a    single    valve,   * 

which,  when  open,  admits  the 
steam  into  the  cylinder,  and 
also  into  the  pipe  which  con- 
nects this  with  the  lower  valve 
box.  The  lower  box  contains 
two  valves,  b  and  c  ;  the  valve 
b,  when  open,  admits  the  steam 
to  pass  from  the  cylinder  above 
the  piston,  by  the  connecting 
tube  to  the  cylinder  below  the 
piston;  the  valve  c,  when  open, 
admits  the  steam  to  pass  from 
below  the  cylinder,  down  into 
the  condenser  d.  This  steam 
entering  the  condenser,  meets 
the  jet  of  water  through  the  valve  d,  where  it  is  condensed. 
The  valve  e,  opening  outwards,  permits  any  steam  which  is 
not  condensed,  together  with  such  atmospheric  air  as  is  ac- 
cumulated, to  pass  away. 

The  valve  a  is  called  the  upper  steam  valve  ;  b,  the  lower 
steam  valve  ;  c,  the  exhausting  valve,  and  d,  the  condensing 
valve. 

583.  Now  let  us  see  in  what  manner  this  machine  will 
produce  the  alternate  ascent  and  descent  of  the  piston. 

In  the  first  place,  all  the  air  which  fills  the  cylinder  and 
tubes  must 'be  expelled.  To  do  this,  the  valves  a,  b,  and  c, 
must  be  opened.  The  steam  will  pass  through  the  pipe  st 
into  the  upper  part  of  the  cylinder,  and  along  the  tube  down 
through  the  valves  b  and  c  into  the  condenser  d.  After  the 
steam  ceases  to  be  condensed  by  the.  cold  of  the  apparatus, 
it  will  rush  out,  mixed  with  air,  through  the  valve  e,  which 
opens  outwards. 

584.  The  apparatus  is  thus  filled  with  steam,  and  all  the 


What  are  the  ste'uons,  names,  and  uses,  of  the  valves  in  fig.  119? 


STEAM  ENGINE.  153 

valves  are  now  to  be  closed ;  but  in  a  few  minutes  a  vacuum 
will  be  formed  in  the  condenser,  by  the  cold  surface  of  that 
vessel. 

The  apparatus  being  in  this  state,  let  the  upper  steam 
valve  a,  the  exhausting  valve  c,  and  the  condensing  valve  d, 
be  opened.  Steam  will  thus  be  admitted  through  a,  to  press 
upon  the  top  of  the  piston,  the  steam  being  prevented  from 
circulating  below  the  piston,  by  the  valve  b  being  closed. 
But  the  steam  below  the  piston  will  rush  through  the  ex- 
hausting valve  c,  into  the  condenser,  where  a  jet  of  cold 
water  through  the  condensing  valve  d,  will  instantly  con- 
dense it,  and  thus  leave  a  vacuum  below  the  piston  in  the 
cylinder.  Into  this  vacuum  the  piston  is  instantly  pressed 
by  the  action  of  the  steam  in  the  upper  part  of  the  cylinder. 

585.  When  the  piston  has  thus  been  forced  to  the  bottom 
of  the  cylinder,  let  the  valves  a,  c,  and  d,  be  closed,  and  let 
the  lower  steam  valve  b  be  opened.     The  effect  of  this  will 
be,  that  the  further  ingress  of  steam  will  be  stopped,  and  the 
further  condensation  of  steam  will  cease,  and  thus  the  steam 
which  is  shut  within  the  apparatus,  will  press  equally  on  all 
sides,  so  that  the  pressure  on  the  upper  and  under  sides  of 
the  piston  will  be  equal.     Thus  there  is  no  force  to  restrain 
the  piston  at  the  bottom  of  the  cylinder,  except  its  weight, 
which  is  more  than  balanced  by  the  weight  of  the  pump-rod 
at  the  other  end  of  the  beam,  and  by  the  preponderance  of 
which  the  piston  rises,  as  in  the  atmospheric  engine. 

586.  When  the  piston  has  arrived  to  the  top  of  the  cylin- 
der, the  valves  a,  c,  and  d,  are  again  opened,  when  steam 
again  presses  on  the  top  of  the  piston,  while  a  vacuum  is 
formed  below  it,  into  which  the  piston  is  driven,  as  already 
shown,  and  so  on  continually. 

The  valves  of  this  engine  were  opened  and  closed  by  lev- 
ers, which  were  worked  by  the  movement  of  the  machine- 
ry. These,  being  unnecessary  to  explain  the  principle,  are 
not  shown  in  the  drawing. 

587.  Mr.  Watt  called  this  his  single  acting  engine,  be- 
cause the  steam  acted  only  above  the  piston,  and  for  the  pur- 
pose of  distinguishing  it  from  his  double  acting  engine,  in 
which  the  piston  was  moved  in  both  directions,  by  the  force 
of  steam. 

588.  Double  Acting  Steam  Engine: — After  the  construc- 
tion of  the  steam  engine  above  described,  Mr.  Watt  conth> 

Explain  the  manner  in  which  this  engine  acts  by  means  of  the  fig- 
ure. Why  does  Mr.  Watt  call  this  his  single  acting  engine  ? 


154  STEAM  ENGINE. 

ued  his  improvements  and  inventions,  which  resulted  in  the 
production  of  his  double  acting  engine.  This  consisted  in 
changing1  the  steam  alternately  from  below,  to  above  the  pis- 
ton, and  at  the  same  time  forming  a  vacuum  alternately  in 
each  end  of  the  cylinder,  into  which  the  piston  was  forced. 
Thus  the  piston  being  at  the  top  of  the  cylinder,  steam  was 
introduced  from  the  boiler  above  it,  while  the  steam  in  the 
cylinder  below  it  was  condensed.  The  piston  was  therefore 
pressed  by  the  steam  above  it  into  a  vacuum  below.  Hav- 
ing arrived  at  the  bottom  of  the  cylinder,  the  steam  was 
changed  in  its  direction,  and  sent  below  the  piston,  while  a 
communication  was  formed  between  the  upper  part  of  the 
cylinder  and  the  condenser,  and  thus  a  vacuum  was  formed 
above  the  piston,  into  which  it  was  forced  by  the  steam  act- 
ing below  it.  In  this  manner  was  the  piston  moved  by  al- 
ternately substituting  steam  for  a  vacuum,  and  a  vacuum  for 
steam,  on  each  side  of  the  piston. 

589.  Circular  motion  of  machinery  by  means  of  steam. 
— The  action  of  the  atmospheric  engine  of  Newcomen,  and 
of  the  improved,  or  single  acting  one  of  Watt,  was  such  as 
could  not  be  applied  to  the  continued  motion  of  machinery. 
Their  motions  were  well  calculated  to  raise  water  from  the 
mines  by  pumping,  and  for  this  purpose  they  were  chiefly 
employed.     Nor  could  these  engines  give  a  perpetual  cir- 
cular, motion,  without  some  changes  in  their  action,  and  ad- 
ditions to  their  machinery.     It  is  obvious,  that  the  extended 
use  of  steam  in  driving  machinery,  absolutely  required  such 
a  motion,  and  it  appears  that  the  genius  of  Watt,  soon  after 
his  experiments  commenced,  saw  the  vast  consequences  of 
such  an  application  of  this  power,  and  he  applied  himself  to 
the  invention  of  machinery  for  this  purpose  accordingly. 

590.  In  Newcomen's  and  Watt's  first  engines,  the  end 
of  the  beam  opposite  to  the  piston  could  only  be  employed 
in  lifting,  since  the  power  was  applied  only  to  force  the 
piston  downwards.     But  in  the  double  acting  engine,  the 
power  of  steam  was  applied  to  the  piston  in  both  directions, 
and  hence  the  opposite  end  of  the  beam  had  a  force  down- 
ward, as  well  as  upward.     If,  therefore,  instead  of  chains, 
rods  of  iron  were  attached  to  each  arch  head  of  the  beam, 
the  one  rod  connected  with  the  piston,  and  the  other  with 

Describe  Watt's  double  acting  steam  engine.  What  is  said  of  the 
action  of  Newcomen's  and  Watt's  first  engine  ?  Why  were  not  their 
motions  applicable  to  machinery  1  Explain  the  reason  why  Watt's 
double  acting  engine  was  applicable  to  the  rotation  of  machinery, 
while  his  other  engine  was  not. 


STEAM  ENGINE. 


155 


machinery  to  be  moved,  it  is  plain  that  since  the  end  of  the 
beam,  connected  with  the  piston,  would  be  pushed  up  and 
drawn  down  with  a  force  equal  to  the  power  of  the  steam 
applied,  the  other  end  of  the  beam  would  act  with  equal 
force,  and  thus  that  a  sufficient  power  might  be  obtained  in 
both  directions. 

591.  The  question  with  respect  to  the  means  by  which  a 
continued  circular  motion  might  be  obtained  from  the  alter- 
nate motion  of  the  working  end  of  the  beam,  did  not  remain 
long  unsettled  in  the  fertile  mind  of  Watt.     A  crank  con- 
nected with  the  end  of  the  beam  by  an  inflexible  or  metalic 
rod,  would  convert  its  up  and  down  motion  into  one  of  at 
least  partial,  rotation. 

592.  But  still  there  remained  a  difficulty  to  be  overcome 
with  respect  to  the  rotation  of  a  crank,  for  there  are  two  po- 
sitions in  which  the  vertical  motions  of  the  working  rod 
could  give  it  no  motion  whatever.      These  are,  when  the 
axis  of    the   crank  a,  fig.   120,  Fig.  120. 

the  joint  of  the  crank  b,  and  the 
working  rod,  or  connector,  with 
the  working  beam  c,  are  in  the 
same  right  line  as  shown  in  the 
figure.  In  this  case  it  is  plain, 
that  the  vertical  action  of  c  could 
not  move  the  crank  in  any  direc- 
tion. Again,  when  the  joint 
b  is  turned  down  to  d,  so  as  to 
bring  the  working  rod  c,  di- 1 
rectly  over  the  crank,  it  will  be 
obvious  that  the  upward  or  down- 
ward force  of  the  beam,  could 
not  give  a  any  motion  what- 
ever. 

Hence,  in  these  two  positions 
the  engine  could  have  no  effect  in  turning  the  crank,  and, 
therefore,  twice  in  every  revolution,  unless  some  remedy 
could  be  found  for  this  defect,  the  whole  machine  must 
cease  to  act. 

593.  Now,  under  Inertia,  (21)  we  have  shown  that  bod- 
ies, when  once  put  in  motion,  have  a  tendency  to  continue 
that  motion,  and  will  do  so,  unless  stopped  by  some  oppos- 

Explain  the  reason  why  a  crank  motion  alone  can  not  be  converted 
into  a  continued  rotation?  In  what  manner  was  the  crank  motion 
converted  into  one  of  perpetual  rotation  7 


156 


STEAM  ENGINE. 


ing  force.  With  respect  to  circular  motion,  this  subject  is 
sufficiently  illustrated  by  the  turning  of  a  coach  wheel  on 
its  axis  when  raised  from  the  ground.  Every  one  knows 
that  when  a  wheel  is  set  in  motion,  under  such  circum- 
stances, it  will  continue  to  revolve  by  its  own  inertia  for 
some  time,  without  any  new  impulse. 

594.  This  principle  Watt  applied  to  continue  the  motion 
of  the  crank.     A  large  heavy  iron  wheel  was  fixed  to  the 
axis  of  the  crank,  which  wheel  being  put  in  motion  by  the 
machinery,  had  the  effect  to  turn  the  crank  beyond  the  po- 
sition in  which  we  have  shown  the  working  rod  had  no 
power  to  move  it,  and  thus  enabled  the  working  rod  to  con- 
tinue the  rotation. 

595.  Such  a  wheel,  called  the  fly  wheel,  or  balance 
wheel,  is  represented  attached  to  the  crank  in  fig.  120,  arid 
is  now  universally  employed  in  all  steam  engines  used  in 
driving  machinery. 

596.  Governor,  or  Regulator. — In    the   application  of 
steam  to  machinery  for  various  purposes,  a  steady  or  equal 
motion  is  highly  important ;  and  although  the  fly  wheel, 
just  described,  had  the  effect  to  equalize  the  motion  of  the 
engine  when  the  power  and  the  resistance  were  the  same, 
yet  when  the  steam  was  increased,  or  the  resistance  dimin- 
ished or  increased,  there  was  no  longer  a  uniform  velocity 
in  the  working  part  of  the  engine. 

In  order  to  remedy  this  defect,  Mr.  Watt  applied  to  his 
engines  an  apparatus  called  a  governor,  and  by  which  the 
quantity  of  steam  admitted  to  the  cylinder  was  so  regulated 
as  to  keep  the  velocity  of  the  engine  nearly  the  same  at  all 
times. 

597.  Of  all  the  contrivances  for  regulating  the  motion  of 
machinery,  this  is  said  to  be  the  most  effectual.     It  will  be 
readily  understood  by  the  following  description  of  fig.  121. 
It  consists  of  two  heavy  iron  Fig.  121. 

balls  />,  attached  to  the  ex- 
tremities of  the  two  rods  b,  e. 
These  rods  play  on  a  joint 
at  e,  passing  through  a  mor- 
tise in  the  vertical  stem  d, 
d.  At  /  these  pieces  are 
united,  by  joints  to  the  twoj( 
short  rods  f,  h,  which,  at 
their,  upper  ends,  are  again 

Give  a  general  description  of  the  Governor,  by  means  of  the  figure. 


STEAM  ENGINE.  157 

connected  by  joints  at  h,  to  a  ring  which  slides  upon  the 
vertical  stem  d  d.  Now  it  will  be  apparent  that  when  these 
balls  are  thrown  outward,  the  lower  links  connected  atft 
will  be  made  to  diverge,  in  consequence  of  which  the  up- 
per links  will  be  drawn  down  the  ring  with  which  they  are 
connected  at  h.  With  this  ring  at  i  is  connected  a  lever 
having  its  axis  at  g,  and  to  the  other  extremity  of  which,  at 
k,  is  fastened  a  vertical  piece,  which  is  connected  by  a  joint 
to  the  valve  v.  To  the  lower  part  of  the  vertical  spindle  d, 
is  attached  a  grooved  wheel  w,  around  which  a  strap  passes, 
which  is  connected  with  the  axis  of  the  fly  wheel. 

598.  Now  when  it  so  happens  that  the  quantity  of  steam 
is  too  great,  the  motion  of  the  fly  wheel  will  give  a  pro- 
portionate velocity  to  the  spindle  d,  d,  by  means  of  the  strap 
around  w,  and  by  which  the  balls,  by  their  centrifugal  force, 
will  be  widely  separated  ;  in  consequence  of  which  the  ring 
h  will  be  drawn  down.     This  will  elevate  the  arm  of  the 
lever  7c,  and  by  which  the  end  i,  of  the  short  lever,  connected 
with  the  valve  v,  in  the  steam  pipe,  will  be  raised,  and  thus 
the  valve  turned  so  as  to  diminish  the  quantity  of  steam  ad- 
mitted to  the  piston.     When  the  motion  of  the  engine  is 
slow,  a  contrary  effect  will  be  produced,  and  the  valve  turn- 
ed so  that  more  steam  will  be  admitted  to  the  engine. 

599.  Low  and  High  pressure  Engines. — After  having 
given  a  description  of  Watt's  double  acting  engine,  it  will 
hardly  be  necessary  to  describe  those  of  the  present  day, 
since  though  they  have  some  additional  apparatus,  still  the 
principle  of  action  is  the  same  in  both,  and  it  is  this,  rather 
than  details,  with  which  it  is  our  object  to  make  the  student 
acquainted. 

600.  To  comprehend  the  working  of  the  piston,  which  is 
usually  hid  from  the  eye  of  the  observer,  it  is  only  neces- 
sary to  remember,  that  in  the  upper  valve  box  there  are  two 
valves,  called  the  upper  steam  valve,  and  the  upper  exhaust- 
ing valve  ;  and  that  in  the  lower  steam  box,  or  bottom  of  the 
cylinder,  there  are  also  two  valves,  called  the  lower  steam 
valve,  and  the  lower  exhausting  valve. 

601.  Now  suppose  the  piston  to  be  at  the  top  of  the  cylin- 
der, the  cylinder  below  it  being  filled  with  steam,  which 
has  just  pressed  the  piston  up.     Then  let  the  upper  steam 

What  is  the  difference  between  Watt's  double  acting  engine  and 
those  of  the  present  day  1     What  are  the  valves  called  in  the  upper, 
and  what  in  the  lower  valve  box  1     When  the  piston  is  at  the  toj.  of 
the  cylinder,  what  valves  are  opened  1 
14 


158  STEAM  ENGINE. 

valve,  and  the  lower  exhausting  valve  be  opened,  the  otin-i 
two  being  closed;  the  steam  which  fills  the  cylinder  below 
the  piston,  will  thus  be  allowed  to  pass  through  the  ex- 
hausting valve  into  the  condenser,  and  a  vacuum  will  be  form- 
ed below  the  piston.  At  the  same  time,  the  upper  steam, 
valve  being  open,  steam  will  be  admitted  above  the  piston 
to  press  it  down  into  the  vacuum,  which  has  been  formed 
below.  On  the  arrival  of  the  piston  to  the  bottom  of  the 
cylinder,  the  upper  steam  valve,  and  the  lower  exhausting 
valve  are  closed,  and  the  lower  steam  valve,  and  upper  ex- 
hausting valve  are  opened,  on  which  the  steam  above  the 
piston  is  condensed,  while  steam  is  admitted  below  the  piston 
to  press  it  into  the  vacuum  thus  formed,  and  so  on  continu- 
ally. 

602.  The  upper  steam  valve,  and  lower  exhausting  valve, 
are  opened  at  the  same  time  ;  the  same  being  the  case  with 
the  lower  steam  valve,  and  upper  exhausting  valve. 

603.  The  above  is  a  description  of  the  movement  of  what 
is  known  under  the  name  of  the  low  pressure  engine,  in 
which  the  steam  is  condensed,  and  a  vacuum  formed,  alter- 
nately, above  and  below  the  piston.     To  this  engine  there 
must  be  attached  a  cold  water  pump  and  cistern,  for  the 
condensation  of  the  steam;  an   air  pump  for  the   removal 
of  the  air  and  condensed  water,  and  a  condenser,  into  which 
a  jet  of  cold  water  is  thrown  to  condense  the  steam. 

604.  In  the  high  pressure  engines,  the  piston  is  pressed 
up  and  down  by  the  force  of  the  steam  alone,  and  without 
the  assistance  of  a  vacuum.     The  additional  power  of  steam 
required  for  this  purpose  is  very  considerable,  being  equal 
to  the  entire  pressure  of  the  atmosphere  on  the  surface  of 
the  piston.     We  have  already  had  occasion  to  show  that  on 
a  piston  of  13  inches  in  diameter,  the  pressure  of  the  atmo- 
sphere amounts  to  nearly  two  tons. 

605.  Now  in  the  low  pressure  engine,  in  which  a  vacuum 
is  formed  on  one  side  of  the  piston,  the  force  of  steam  re- 
quired to  move  it  is  diminished  by  the  amount  of  atmo 
spheric  pressure  equal  to  the  size  of  the  piston. 

606.  But  in  the  high  pressure  engine,  the  piston  works 
in  both  directions  against  the  weight  of  the  atmosphere,  and 
hence  requires  an  additional  power  of  steam  equal  to  the 
weight  of  the  atmosphere  on  the  piston. 

When  at  the  bottom,  whr*t  valves  are  opened  7  What  constitutes  a 
low  pressure  engine  ?  How  much  more  force  of  steam  is  required  in 
high  than  in  low  pressure  engines? 


ACOUSTICS.  159 

607.  These  engines  are,  however,  much  more  simple  and 
cheap  than  the  low  pressure,  since  the  condenser,  cold  water 
pump,  air  pump,  and  cold  water  cistern,  are  dispensed  with , 
nothing  more  being  necessary  than  the  boiler,  cylinder,  pis- 
ton, and  valves.     Hence  for  rail-roads,  and  all  locomotive 
purposes,  the  high  pressure  engines  are,  and  must  be  used. 

608.  With  respect  to  engines  used  on  board  of  steam- 
boats, the  low  pressure  are  universally  employed  by  the 
English,  and  it  is  well  known,  that  few  accidents  from  the 
bursting  of  machinery  have  ever  happened  in  that  country. 
In  most  of  their  boats  two  engines  are  used,  each  of  which 
turns  a  crank,  and  thus  the  necessity  of  a  fly  wheel  is 
avoided. 

In  this  country  high  pressure  engines  are  in  common 
use  for  boats,  though  they  are  not  universally  employed.  In 
some,  two  engines  are  worked,  and  the  fly  wheel  dispensed 
with,  as  in  England. 

609.  The  great  number  of  accidents  which  have  happen- 
ed in  this  country,  whether  on  board  of  low  or  high  press- 
ure boats,  must  be  attributed,  in  a  great  measure,  to  the 
eagerness  of  our  countrymen  to  be  transported  from  place  to 
place  with  the  greatest  possible  speed,  all  thoughts  of  safety 
being  absorbed  in  this  passion.     It  is,  however,  true,  from 
the  very  nature  of  the  case,  that  there  is  far  greater  danger 
from  the  bursting  of  the  machinery  in  the  high,  than  in  the 
low  pressure  engines,  since  not  only  the  cylinder,  but  the 
boiler  and  steam  pipes,  must  sustain  a  much  higher  pressure 
in  order  to  gain  the  same  speed,  other  circumstances  being 
equal. 

ACOUSTICS. 

610.  Acoustics   is  that  branch   of  natural   philosophy 
which   treats   of  the   origin,   propagation,   and   effects   of 
sound. 

6 11-.  When  a  sonorous,  or  sounding  body  is  struck,  it  is 
thrown  into  a  tremulous,  or  vibrating  motion.  This  mo- 
tion is  communicated  to  the  air  which  surrounds  us,  and  by 
ihe  air  is  conveyed  to  our  ear  drums,  which  also  undergo  a 
vibratory  motion,  and  this  last  motion,  throwing  the  audi- 
tory nerves  into  action,  we  thereby  gain  the  sensation  of 
sound. 

What  parts  are  dispensed  with  in  high  pressure  engines'?  What  is 
acoustics  1  When  a  sonorous  body  is  struck  within  hearing,  in  what 
manner  do  we  gain  from  it  the  sensation  of  sound  ? 


160  ACOUSTICS. 

612.  If  any  sounding  body,  of  considerable  size,  is  sus- 
pended in  the  air  and  struck,  this  tremulous  motion  is  dis- 
tinctly visible  to  the  eye,  and  while  the  eye  perceives  its  mo- 
tion, the  ear  perceives  the  sound. 

613.  That  sound  is  conveyed  to  the  ear  by  the  motion 
which  the  sounding  body  communicates  to  the  air,  is  proved 
by  an  interesting  experiment  with  the  air  pump.     Among 
philosophical  instruments,  there  is  a  small  bell,  the  hammer 
of  which  is  moved  by  a  spring  connected  with  clock-work, 
and  which  is  made  expressly  for  this  experiment. 

If  this  instrument  be  wound  up,  and  placed  under  the  re- 
ceiver of  an  air  pump,  the  sound  of  the  bell  may  at  first  be 
heard  to  a  considerable  distance,  but  as  the  air  is  exhausted, 
it  becomes  less  and  less  audible,  until  no  longer  to  be  heard, 
the  strokes  of  the  hammer,  though  seen  by  the  eye,  produ- 
cing no  effect  upon  the  ear.  Upon  allowing  the  air  to  re- 
turn gradually,  a  faint  sound  is  at  first  heard,  which  be- 
comes louder  and  louder,  until  as  much  air  is  admitted  as 
was  withdrawn. 

614.  On  the  contrary,  when  the  air  is  more  dense  than 
ordinary,  or  when  a  greater  quantity  is  contained  in  a  ves- 
sel, than  in  the  same  space  in  the  open  air,  the  effect  of 
sound  on  the  ear  is  increased.     This  is  illustrated  by  the 
use  of  the  diving  bell. 

The  diving  bell  is  a  large  vessel,  open  at  the  bottom,  un- 
der which  men  descend  to  the  beds  of  rivers,  for  the  pur- 
pose of  obtaining  articles  from  the  wrecks  of  vessels.  When 
this  machine  is  sunk  to  any  considerable  depth,  the  water 
above,  by  its  pressure,  condenses  the  air  under  it  with  great 
force.  In  this  situation,  a  whisper  is  as  loud  as  a  common 
voice  in  the  open  air,  and  an  ordinary  voice  becomes  pain 
ful  to  the  ear. 

615.  Again,  on  the  tops  of  high  mountains,  where  the 
pressure,  or  density,  of  the  air  is  much  less  than  on  the  sur 
face  of  the  earth,  the  report  of  a  pistol  is  heard  only  a  few 
rods,  and  the  human  voice  is  so  weak  as  to  be  inaudible  at 
ordinary  distances. 

Thus,  the  atmosphere  which  surrounds  us,  is  the  medium 
by  which  sounds  are  conveyed  to  our  ears,  and  to  its  vibra- 


How  is  it  proved  that  sound  is  conveyed  to  the  ear  by  the  medium 
of  the  air  1  When  the  air  is  more  dense  than  ordinary  how  does  it  af- 
fect sound  1  What  is  said  of  the  effects  of  sound  on  the  tops  of  high 
mountains  1 


ACOUSTICS.  161 

tions  we  are  indebted  for  the  sense  of  hearing,  as  well  as  to 
al.  we  enjoy  from  the  charms  of  music. 

616.  The  atmosphere,  though  the  most  common,  is  not. 
however,  the  only,  or  the  best  conductor  of  sound.     Solid 
bodies  conduct  sound  better  than  elastic  fluids.      Hence,  if 
a  person  lay  his  ear  on  a  long  stick  of  timber,  the  scratch 
of  a  pin  may  be  heard  from  the  other  end,  which  could  not 
be  perceived  through  the  air. 

617.  The  earth  conducts    loud  rumbling  sounds   made 
below  its  surface  to  great  distances.     Thus,  it  is  said,  that 
in  countries  where  the  volcanoes  exist,  the  rumbling  noise 
which  generally  precedes  an  eruption,  is  heard  first  by  the 
beasts  of  the  field,  because  their  ears  are  commonly  near  the 
ground,  and  that  by  their  agitation  and  alarm,  they  give 
warning  of  its  approach  to  the  inhabitants. 

The  Indians  of  our  country  will  discover  the  approach  of 
horses  or  men,  by  laying  their  ears  on  the  ground,  when 
they  are  at  such  distances  as  not  to  be  heard  in  any  other 
manner. 

618.  Sound  is  propagated  through  the  air  at  the  rate  of 
1142  feet  in  a  second  of  time.     When  compared  with  the 
velocity  of  light,  it  therefore  moves  but  slowly.     Any  one 
may  be  convinced  of  this  by  watching  the  discharge  of 
cannon  at  a  distance      The  flash  is  seen  apparently  at  the 
instant  the  gunner  touches  fire  to  the  powder;  the  whizzing 
of  the  ball,  if  the  ear  is  in  its  direction,  is  next  heard,  and 
lastly,  the  report. 

Solid  substances  convey  sounds  with  greater  velocity 
than  air,  as  is  proved  by  the  following  experiment,  lately 
made  at  Paris,  by  M.  Riot. 

619.  At  the  extremity  of  a  cylindrical  tube,  upwards  of 
3000  feet  long,  a  ring  of  metai  was  placed,  of  the  same 
diameter  as  the  aperture  of  the  tube;  and  in  the  centre  of 
this  ring,  in  the  mouth  of  the  tube,  was  suspended  a  clock 
bell   and  hammer.     The  hammer  was  made  to  strike  the 
ring  and  the  bell  at  the  same  instant,  so  that  the  sound  of  the 
ring  would  be  transmitted  to  the  remote  end  of  the  tube, 
ihrough  the  conducting  power  of  the  tube  itself,  while  the 
sound  of  the  bell  would  be  transmitted  through  the  medium 

Which  are  the  best  conductors  of  sound,  solid  or  elastic  substances  1 
What  is  said  of  the  earth  as  a  conductor  of  sounds  1  How  is  it  said 
that  the  Indians  discover  the  approach  of  horses  1  How  fast  does 
sound  pass  through  the  air"?  Which  convey  sounds  with  the  greatest 
velocity,  solid  substances  or  air  1 

14* 


162 


ACOUSTICS. 


of  the  air  inclosed  in  the  tube.  The  ear  being  then  placed 
at  the  remote  end  of  the  tube,  the  sound  of  the  ring,  trans- 
mitted by  the  metal  of  the  tube,  was  first  heard  distinctly, 
and  after  a  short  interval  had  elapsed,  the  sound  of  the  bell, 
transmitted  by  the  air  in  the  tube,  was  heard.  The  result 
of  several  experiments  was,  that  the  metal  conducted  the 
sound  at  the  rate  of  about  11,865  feet  per  second,  which  is 
about  ten  and  a  half  times  the  velocity  with  which  it  is  con- 
ducted by  the  air. 

620.  Sound  moves  forward  in  straight  lines,  and  in  this 
respect  follows  the  same  laws  as  moving  bodies,  and  light. 
It  also  follows  the  same  laws  in  being  reflected,  or  thrown 
back,  when  it  strikes  a  solid,  or  reflecting  surface. 

621.  Echo. — If  the  surface  be  smooth,  and  of  considera- 
ble dimensions,  the  sound  will  be  reflected,  and  an  echo  will 
be  heard ;  but  if  the  surface  is  very  irregular,  soft,  or  small, 
no  such  effect  will  be  produced. 

In  order  to  hear  the  echo,  the  ear  must  be  placed  in  a 
certain  direction,  in  respect  to  the  point  where  the  sound  is 
produced,  and  the  reflecting  surface. 

If  a  sound  be  produced  at  a,  fig.  122, 
and  strike  the  plain  surface  b,  it  will  be 
reflected  back  in  the  same  line,  and  the 
echo  will  be  heard  at  c  or  a.  That  is,  the 
angle  under  which  it  approaches  the  re- 
flecting surface,  and  that  under  which  it 
leaves  it,  will  be  equal. 

622.  Whether  the  sound  strikes  the  re- 
flecting surface  at  right  angles,  or  oblique- 
ly, the  angle  of  approach,  and  the  angle 
of  reflection,  will  always  be  the  same,  and 
equal. 


Fig.  122. 
b 


This  is  illustrated  by 
fig.  123,  where  suppose 
a  pistol  to  be  fired  at  a, 
while  the  reflecting  sur- 
face is  at  c  ;  then  the 
echo  will  be  heard  at  b, 
he  angles  2  andl  being 
equal  to  each  other. 


Pig.  123. 


Describe  the  experiment,  proving  that  sound  is  conducted  by  u  metsu 
with  greater  velocity  than  by  the  air.  In  what  lines  does  sound  movel 
From  what  kind  of  surface  is  sound  reflected,  so  as  to  produce  an  echo  1 
Explain  fig.  122.  Explain  fig.  123,  and  show  in  what  direction  sound 
approaches  and  leaves  a  reflecting  surface. 


ACOUSTICS. 


16* 


623.  If  a  sound  be  emitted  between  two  reflecting  sur- 
faces, paiT.llel  to  each  other,  it  will  reverberate,  or  be  an- 
swered backwards  and  forwards  several  times. 

Thus,  if  the  sound  be  made  at  a,  fig.  Fig.  124. 
124,  it  will  not  only  rebound  back  again 
to  a,  but  will  also  be  reflected  from  the 
points  c  and  d,  and  were  such  reflecting 
surfaces  placed  at  every  point  around  a 
circle  from  a,  the  »ound  would  be  thrown 
back  from  them  all,  at  the  same  instant, 
and  would  meet  again  at  the  point  a. 

We  shall  see,  under  the  article  Optics,/ 
that  light  observes  exactly  the  same  law 
in  respect  to  its  reflection  from  plane  suriaces,  and  that  the 
angle  at  which  it  strikes,  is  called  the  angle  of  incidence, 
and  that  under  which  it  leaves  the  reflecting  surface,  is  call- 
ed the  angle  of  reflection.  The  same  terms  are  employed 
in  respect  to  sound. 

624.  In  a  circle,  as  mentioned  above,  sound  is  reflected 
from  every  plane  surface  placed  around  it,  and  hence,  if  the 
sound  is  emitted  from  the  centre  of  a  circle,  this  centre  will 
be  the  point  at  which  the  echo  will  be  most  distinct. 

Suppose  the  ear  to  be  placed 
at  the  point  a,  fig.  125,  in  the 
centre  of  a  circle ;  and  let  a  sound 
be  produced  at  the  same  point, 
then  it  will  move  along  the  line 
a  e,  and  be  reflected  from  the 
plane  surface,  back  on  the  same  d 
line  to  a  ;  and  this  will  take  place 
from  all  the  plane  surfaces  placed 
around  the  circumference  of  a 
circle  ;  and  as  all  these  surfaces 
are  at  the  same  distance  from  the 
centre,  so  the  reflected  sound  will  arrive  at  the  point  &,  at 
the  same  instant;  and  the  echo  will  be  loud,  in  proportion 
to  the  number  and  perfection  of  these  reflecting  surfaces. 

625.  It  is  apparent  that  the  auditor,  in  this  case,  must  be 
placed  in  the  centre  from  which  the  sound  proceeds,  to  re- 


Fig.  125. 
e 


What  is  the  angle  under  which  sound  strikes  a  reflecting  surface 
called'?    What  is  the  angle  under  which  it  leaves  a  reflecting  sur- 
face called'?    Is  there  any  difference  in  the  quantity  of  these  two  aj» 
^lesl    Suppose  a  pistol  to  be  fired  in  the  centre  of  a  circular  room 
wnere  would  be  the  echo?    Explain  fig.  124,  and  give  the  reason. 


164 


ACOUSTICS* 


Fig.  126. 


ceive  the  greatest  effect.  But  if  the  shape  of  the  room  be 
oval,  or  elliptical,  the  sound  may  be  made  in  one  part,  and 
the  echo  will  be  heard  in  another  part,  because  the  ellipse 
has  two  points,  called  foci,  at  one  of  which,  the  sound  being- 
produced,  it  will  be  concentrated  in  the  other. 

Suppose  a  sound  to  be  produced 
at  a,  fig.  126,  it  will  be  reflected 
from  the  sides  of  the  room,  the  angles 
of  incidence  being  equal  to  those  of 
reflection,  and  will  be  concentrated  at 
b.  Hence  a  hearer  standing  at  b,  will 
be  affected  by  the  united  rays  of  sound 
from  different  parts  of  the  room,  so 
that  a  whisper  at  #,  will  become  audi- 
ble at  b,  when  it  would  not  be  heard 
in  any  other  part  of  the  room.  Were 
the  sides  of  the  room  lined  with  a  pol- 
ished metal,  the  rays  of  light  or  heat 
would  be  concentrated  in  the  same 
manner. 

The  reason  of  this  will  be  understood,  when  we  consider, 
that  an  ear,  placed  at  c,  will  receive  only  one  ray  of  the 
sound  proceeding  from  a,  while  if  placed  at  b,  it  will  receive 
the  rays  from  all  parts  of  the  room.  Such  a  room,  whether 
constructed  by  design  or  accident,  would  be  a  whispering 
gallery. 

626.  On  a  smooth  surface,  the  rays,  or  pulses  of  sound, 
will  pass  with  less  impediment  than  on  a  rough  one.     For 
this  reason,  persons  can  talk  to  each  other  on  tho  opposite 
sides  of  a  river,  when  they  could  not  be   understood   to 
the  same  distance  over  the  land.     The  report  of  a  cannon, 
at  sea,  when  the  water  is  smooth,  may  be  heard  at  a  great 
distance,  but  if  the  sea  is  rough,  even   without  wind,  the 
sound  will  be  broken,  and  will  reach  only  half  as  far. 

627.  Musical  Instruments. — The  strings  of  musical  in- 
struments are  elastic  cords,  which  being  fixed  at  each  end, 
produce  sounds  by  vibrating  in  the  middle. 

The  string  of  a  violin,  or  piano,  when  pulled  to  one  side 
by  its  middle,  and  let  go,  vibrates  backwards  and  forwards, 

Suppose  a  sound  to  be  produced  in  one  of  the  foci  of  an  ellipse, 
where  then  might  it  be  distinctly  heard?  Explain  fig.  126,  and  give 
the  reason.  Why  is  it  that  persons  can  converse  on  the  opposite  sides 
of  a  river,  when  they  could  not  hear  each  other  at  the  same  distance 
over  the  land  ?  How  do  the  strings  of  musical  instruments  produce 
sounds  1 


ACOUSTICS.  165 

like  a  pendulum,  and  striking  rapidly  against  the  air,  pro- 
duces tones,  which  are  grave,  or  acute,  according  to  its  ten- 
sion, size,  or  length. 

628.  The  manner  in  which  such  a  string  vibrates,  is 
shown  by  fig.  127. 

If  pulled  from  e 
to  a,  it  will  not  stop 
again  at  e,  but  in 
passing  from  a  to 
e,  it  will  gain  a 
momentum,  which 
will  carry  it  to  c, 
and  in  returning, 

its  momentum  will  again  carry  it  to  d,  and  so  on,  backwards 
and  forwards,  like  a  pendulum,  until  its  tension,  and  the  re- 
sistance of  the  air,  will  finally  bring  it  to  rest. 

The  grave,  or  sharp  tones  of  the  same  string,  depend  on 
its  different  degrees  of  tension;  hence,  if  a  string  be  struck, 
and  while  vibrating,  its  tension  be  increased,  its  tone  will  be 
changed  from  a  lower  to  a  higher  pitch. 

629.  Strings  of  the  same  length  are  made  to  vibrate  slow, 
or  quick,  and  consequently  to  produce  a  variety  of  sounds, 
oy  making  some  larger  than  others,  and  giving  them  dif- 
ferent degrees  of  tension.     The  violin  and  bass  viol  are  fa- 
miliar examples  of  this.     The  low,  or  bass  strings,  are  cov- 
ered with  metallic  wire,  in  order  to  make  their  magnitude 
and  weight  prevent  their  vibrations  from  being  too  rapid, 
and  thus  they  are  made  to  give  deep  or  grave  tones.     The 
o&er  strings  are  diminished  in  thickness,  and  increased  in 
tension,  so  as  to  make  them  produce  a  greater  number  of 
vibrations  in  a  given  time,  and  thus  their  tones  become  sharp, 
or  acute,  in  proportion. 

63G.  Unvler  certain  circumstances,  a  long  string  will  di- 
vide AS^'I  nito  halves,  thirds,  or  quarters,  without  depress- 
ing: any  part  of  it,  and  thus  give  several  harmonious  tones 
at  the  same  time. 

The  fairy  tones  of  the  jEolian  harp  are  produced  in  this 
manner.  This  instrument  consists  of  a  simple  box  of  wood, 
with  four  or  five  strings,  two  or  three  feet  long,  fastened  at 
each  end.  These  are  tuned  in  unison,  so  that  when  made 

Explain  fig.  127.  On  what  do  the  grave  or  acute  tones  of  the  same 
string  depend  1  Why  are  the  bass  strings  of  instruments  covered  with 
metallic  wire  7  Why  is  there  a  variety  of  tones  in  the  JSolian  harp, 
since  all  the  strings  are  tuned  in  unison  7 


166  WIND. 

to  vibrate  with  force,  they  produce  the  same  tones.  But 
when  suspended  in  a  gentle  breeze,  each  string,  according 
to  the  manner  or  force  in  which  it  receives  the  blast,  either 
sounds,  as  •<*  whole,  or  is  divided  into  several  parts,  as  above 
described.  "  The  result  of  which,"  says  Dr.  Arnot,  "  is  the 
production  of  the  most  pleasing  combination,  and  succession 
of  sounds,  that  the  ear  ever  listened  to,  or  fancy  perhaps 
conceived.  After  a  pause,  this  fairy  harp  is  often  heard  be- 
ginning with  a  low  and  solemn  note,  like  the  base  of  dis- 
tant music  in  the  sky ;  the  sound  then  swells  as  if  approach- 
ing, and  other  tones  break  forth,  mingling  with  the  first, 
and  with  each  other." 

631.   The  manner  in  which  a  string  vibrates  in  parts,  will 
be  understood  by  fig.  128. 

Fig.  128. 


Suppose  the  whole  length  of  the  string  to  be  from  a  to  b, 
and  that  it  is  fixed  at  these  two  points.  The  portion  from 
b  to  c,  vibrates  as  though  it  was  fixed  at  c,  and  its  tone  dif- 
fers from  those  of  the  other  parts  of  the  string.  The  same 
happens  from  c  to  d,  and  from  d  to  a.  While  a  string  is 
thus  vibrating,  if  a  small  piece  of  paper  be  laid  on  the  part 
c,  or  d,  it  will  remain,  but  if  placed  on  any  other  part  of 
the  string,  it  will  be  shaken  off. 

WIND. 

632.  Wind  is  nothing  more  than  air  in  motion.     The  use 
of  a  fan,  in  warm  weather,  only  serves  to  move  the  air,  and 
thus  to  make  a  little  breeze  about  the  person  using  it. 

633.  As  a  natural  phenomenon,  that  motion  of  the  air 
which  we  call  wind,  is  produced  in  consequence  of  there 
being  a  greater  degree  of  heat  in  one  place  than  in  another. 
The  air  thus  heated,  rises  upward,  while  that  which  sur- 
rounds this,  moves  forward  to  restore  equilibrium. 

The  truth  of  this  is  illustrated  by  the  fact,  that  during  the 
burning  of  a  house  in  a  calm  night,  the  motion  of  the  air 
toward?  the  place  where  it  is  thus  rarefied,  makes  the  wind 
blow  from  every  point  towards  the  flame. 

Explain  fig.  128,  showing  the  manner  in  which  strings  vibrate  in 
parts.  Wha'  is  wind  7  As  a  natural  phenomenon,  how  is  wind  pro- 
duced, or,  what  is  the  cause  of  wind  1  How  is  this  illustrated  7 


WIND.  167 

634.  In  islands,  situated  in  hot  climates,  this  principle  is 
charmingly  illustrated.     The  land,  during  the  day  time,  be- 
ing under  the  rays  of  a  tropical  sun,  becomes  heated  in  a 
greater  degree  than  the  surrounding  ocean,  and,  consequent- 
ly, there  rises  from  the  land  a  stream  of  warm  air,  during 
the  day,  while  the  cooler  air  from  the  surface  of  the  water, 
moving  forward  to  supply  this  partial  vacancy,  produces  a 
cool  breeze  setting  inland  on  all  sides  of  the  island.     This 
constitutes  the  sea  breeze,  which  is  so  delightful  to  the  in- 
habitants of  those  hot  countries,  and  without  which  men 
could  hardly  exist  in  some  of  the  most  luxuriant  islands  be- 
tween the  tropics. 

During  the  night,  the  motion  of  the  air  is  reversed,  be- 
cause the  earth  being  heated  superficially,  soon  cools  when 
the  sun  is  absent,  while  the  water  being  warmed  several 
feet  below  its  surface,  retains  its  heat  longer. 

Consequently,  towards  morning,  the  earth  becomes  colder 
than  the  water,  and  the  air  sinking  down  upon  it,  seeks  an 
equilibrium,  by  flowing  outwards,  like  rays  from  a  centre, 
and  thus  the  land  breeze  is  produced. 

The  wind  then  continues  to  blow  from  the  land  until  the 
equilibrium  is  restored,  or  until  the  morning  sun  makes  the 
land  of  the  same  temperature  as  the  water,  when  for  a  time 
there  will  be  a  dead  calm.  Then  again  the  land  becoming 
warmer  than  the  water,  the  sea  breeze  returns  as  before, 
and  thus  the  inhabitants  of  those  sultry  climates  are  con- 
stantly refreshed  during  the  summer  season,  with  alternate 
land  and  sea  breezes. 

635.  At  the  equator,  which  is  a  part  of  the  earth  con- 
tinually under  the  heat  of  a  burning  sun,  the  air  is  expand- 
ed, ana1  ascends  upwards,  so  as  to  produce  currents  from  the 
north  and  south,  which  move  forward  to  supply  the  place 
of  the  heated  air  as  it  rises.     These  two  currents,  coming 
from  latitudes  where  the  daily  motion  of  the  earth  is  less 
than  at  the  equator,  do  not  obtain  its  full  rate  of  motion,  and 
therefore,  when  they  approach  the  equator,  do  not  move  so 
fast  eastward  as  that  portion  of  the  earth,  by  the  difference 
between  the  equator's  velocity,  and  that  of  the  latitudes  from 
which  they  come.     This  wind  therefore  falls  behind  the 
earth  in  her  diurnal  motion,  and,  consequently,  has  a  rela- 

In  the  islands  of  hot  climates,  why  does  the  wind  blow  inland  du- 
ring the  day,  and  off  the  land  during  the  night'?  What  are  these 
breezes  called  1  What  is  said  of  the  ascent  of  heated  air  at  the  equa- 
tor? What  is  the  consequence  on  the  air  towards  the  north  and  south? 


168  WIND. 

live  motion  towards  the  west.  This  constant  breeze  towards 
the  west  is  called  the  trade  wind,  because  a  large  portion 
of  the  commerce  of  nations  comes  within  its  influence. 

636.  While  the  air  in  the  lower  regions  of  the  atmosphere 
is  thus  constantly  flowing  from  the  north  and  south  towards 
the  equator,  and  forming  the  trade  winds  between  the  trop- 
ics, the  .heated  air  from  these  regions  as  perpetually  rises, 
and  forms  a  counter  current  through  the  higher  regions,  to- 
wards the  north  and  south  from  the  tropics,  thus  restoring 
the  equilibrium. 

637.  This  counter  motion  of  the  air  in  the  upper  and  low- 
er regions  is  illustrated  by  a  very  simple  experiment.     Open 
a  door  a  few  inches,  leading  into  a  heated  room,  and  hold  a 
lighted  candle  at  the  top  of  the  passage ;  the  current  of  air. 
as  indicated  by  the  direction  of  the  flame,  will  be  out  of  the 
room.     Then  set  the  candle  on  the  floor,  and  it  will  show 
that  the  current  is  there  into  the  room.     Thus,  while  the 
heated  air  rises  and  passes  out  of  the  room,  that  which  is 
colder  flows  in,  along  the  floor,  to  take  its  place. 

This  explains  the  reason  why  our  feet  are  apt  to  suffer 
with  the  cold,  in  a  room  moderately  heated,  while  the  other 
parts  of  the  body  are  comfortable.  It  also  explains  why 
those  who  sit  in  the  gallery  of  a  church  are  sufficiently 
warm,  while  those  who  sit  below  may  be  sh'vering  with 
the  cold. 

638.  From  such  facts,  showing  the  tendency  of  heated 
air  to  ascend,  while  that  which  is  colder  moves  forward  to 
supply  its  place,  it  is  easy  to  account  for  the  reason  why  th^ 
wind  blows  perpetually  from  the  north  and  south  towards? 
the  tropics;  for,  the  air  being  heated,  as  stated  above,  it  as- 
cends, and  then  flows  north  and  south  towards  the  polos, 
until,  growing  cold,  it  sinks  down,  and  again  flows  towards 
the  equator. 

639.  Perhaps  these  opposite  motions  of  the  two  currents 
will  be  better  understood  by  the  sketch,  figure  129. 

Suppose  a  b  c  to  represent  a  portion  of  the  earth's  sur- 
face, a  being  towards  the  north  pole,  >c  towards  the  south 
pole,  and  b  the  equator.  The  currents  of  air  are  supposec 
to  pass  in  the  direction  of  the  arrows.  The  wind,  therefore 
from  a  to  b  would  blow,  on  the  surface  of  the  earth,  from 

How  are  the  trade  winds  formed  1  While  the  air  in  the  lower  re- 
gions  flows  from  the  north  and  south  towards  the  equator,  in  what  di- 
rection does  it  flow  in  higher  regions  1  How  is  this  counter  current  (r 
Unvcr  and  upper  regions  illustrated  by  a  simple  experiment  1 


OPTICS.  169 


north  to  south,  while  from  e  to  a,  the  upper  current  would 
pass  from  south  to  north,  until  it  came  to  a,  when  it  would 
change  its  direction  towards  the  south.  The  currents  in 
the  southern  hemisphere  being  governed  by  the  same  laws, 
would  assume  similar  directions. 

OPTICS. 

640.  Optics  is  that  science  which  treats  of  vision,  and  the 
properties  and  phenomena  of  light. 

The  term  optics  is  derived  from  a  Greek  word,  which 
signifies  seeing. 

This  science  involves  some  of  the  most  elegant  and  im- 
portant branches  of  natural  philosophy.  It  presents  us  with 
experiments  which  are  attractive  by  their  beauty,  and  which 
astonish  us  by  their  novelty ;  and,  at  the  same  time,  it  inves- 
tigates the  principles  of  some  of  the  most  useful  among  the 
articles  of  common  life. 

641.  There  are  two  opinions  concerning  the  nature  of 
light.     Some  maintain  that  it  is  composed  of  material  parti- 
cles, which  are  constantly  thrown  off  from  the  luminous 
body  ;  while  others  suppose  that  it  is  a  fluid  diffused  through 
all  nature,  and  that  the  luminous,  or  burning  body,  occa- 
sions waves  or  undulations  in  this  fluid,  by  which  the  light 
is  propagated  in  the  same  manner  as  sound  is  conveyed 
through  the  air.     The  most  probable  opinion,  however,  is, 
that  light  is  composed  of  exceedingly  minute  particles  of 
matter.     But  whatever  may  be  the  nature  or  cause  of  light, 
it  has  certain  general  properties  or  effects  which  we  can 
investigate.     Thus,  by  experiments,  we  can  determine  the 
laws  by  which  it  is  governed  in  its  passage  through  differ- 

What  common  fact  does  this  experiment  illustrate  1  Define  Optics  1 
What  is  said  of  the  elegance  and  importance  of  this  science'?  Wha; 
are  the  two  opinions  concerning  the  nature  of  light  1  What  is  the 
most  probable  opinion  1 

15 


170  OPTICS. 

ent  transparent  substances,  and  also  those  by  which  it  is 
governed  when  it  strikes  a  substance  through  which  it  can- 
not pass.  We  can  likewise  test  its  nature  to  a  certain  de- 
gree, by  decomposing  or  dividing  it  into  its  elementary 
parts,  as  the  chemist  decomposes  any  substance  he  wishes 
to  analyze. 

642.  To  understand  the  science  of  optics,  it  is  necessary 
to  define  several  terms,  which,  although  some  of  them  may 
be  in  common  use,  have  a  technical  meaning,  when  applied 
to  this  science. 

a.  Light  is  that  principle,  or  substance,  which  enables 
us  to  see  any  body  from  which  it  proceeds.     If  a  luminous 
substance,  as  a  burning  candle,  be  carried  into  a  dark  room, 
the  objects  in  the  room  become  visible,  because  they  reflect 
the  light  of  the  candle  to  our  eyes. 

b.  Luminous  bodies  are  such  as  emit  light  from  their  own 
substance.      The  sun,  fire,  and  phosphorus,  are  luminous 
bodies.    The  moon,  and  the  other  planets,  are  not  luminous, 
since  they  borrow  their  light  from  the  sun. 

c.  Transparent  bodies  are  such  as  permit  the  rays  of 
light  to  pass  freely  through  them.     Air  and  some  of  the 
gasses  are  perfectly  transparent,  since  they  transmit  light 
without  being  visible  themselves.    Glass  and  water  are  also 
considered  transparent,  but  they  are  not  perfectly  so,  since 
they  are  themselves  visible,  and  therefore  do  not  suffer  the 
light  to  pass  through  them  without  interruption. 

d.  Translucent  bodies  are  such  as  permit  the  light  to 
pass,  but  not  in  sufficient  quantity  to  render  objects  distinct, 
when  seen  through  them. 

e.  Opaque  is  the  reverse  of  transparent.  Any  body  which 
permits  none  of  the  rays  of  light  to  pass  through  it,  is 
opaque. 

/  Illuminated,  enlightened.  Any  thing  is  illuminated 
when  the  light  shines  upon  it,  so  as  to  make  it  visible. 
Every  object  exposed  to  the  sun  is  illuminated.  A  lamp 
illuminates  a  room,  and  every  thing  in  it. 

g.  A  Ray  is  a  single  line  of  light,  as  it  comes  from  a  lu- 
minous body. 


What  is  light  1  What  is  a  luminous  body  1  What  is  a  transpa- 
rent body  7  Are  glass  and  water  perfectly  transparent  1  How  is  it 
proved  that  air  is  perfectly  transparent  1  What  are  translucent  bod- 
ies 1  What  are  opaque  bodies  1  What  is  meant  by  illumir\ated  ? 
What  is  a  ray  of  light  1 


OPTICS.  17] 

n,  A  Beam  of  light  is  a  body  of  parallel  rays. 

i.  A  Pencil  of  light  is  a  body  of  diverging  or  converging 
rays. 

k.  Divergent  rays,  are  such  as  come  from  a  point,  and 
continually  separate  wider  apart,  as  they  proceed. 

/.  Convergent  rays,  are  those  which  approach  each 
other,  so  as  to  meet  at  a  common  point. 

m.  Luminous  bodies  emit  rays,  or  pencils  of  light,  in 
every  direction,  so  that  the  space  through  which  they  are 
visible  is  filled  with  them  at  every  possible  point. 

643.  Thus,  the  sun   illuminates  every  point   of  space, 
within  the  whole  solar  system.     A  light,  as  that  of  a  light 
house,  which  can  be  seen  from  the  distance  of  ten  miles  in 
one  direction,  fills  every  point  in  a  circuit  of  ten  miles  from 
it,  with  light.     Were  this  not  the  case,  the  light  from  it 
could  not  be  seen  from  every  point  within  that  circumfer- 
ence. 

644.  The  rays  of  light  move  forward  in  straight  lines 
from  the  luminous  body,  and  are  never  turned  out  of  their 
course  except  by  some  obstacle. 

Let     a,     fig.  Fig.  130. 

130,  be  a  beam 
of  light  from  the 
sun  passing 
through  a  small 
orifice  in  the 
window  shutter 

b.  The  sun  cannot  be  seen  through  the  crooked  tube  e, 
because  the  beam  passing  in  a  straight  line,  strikes  the  side 
of  the  tube,  and  therefore  does  not  pass  through  it. 

645.  All  the  illuminated  bodies,  whether  natural  or  arti- 
ficial, throw  off  light  in  every  direction  of  the  same  color  as 
themselves,  though  the  light  with  which  they  are  illumi- 
nated is  white  or  without  colour. 

This  fact  is  obvious  to  all  who  are  endowed  with  sight. 
Thus,  the  light  proceeding  from  grass  is  green,  while  that 
proceeding  from  a  rose  is  red,  and  so  of  every  other  colour. 

What  is  a  beam  1  What  a  pencil  1  What  are  divergent  rays  7 
What  are  convergent  rays'?  In  what  direction  do  luminous  bodies 
emit  light  1  How  is  it  proved  that  a  luminous  body  fills  every  point 
within  a  certain  distance  with  light  1  Why  cannot  a  beam  of  light  be 
seen  through  a  bent  tube"?  What  is  the  colour  of  the  light  which  dif- 
ferent bodies  throw  ""*  " 
of  the  other  rays'? 


172  OPTICS. 

We  shall  be  convinced,  in  another  place,  that  the 
light  with  which  things  are  illuminated,  is  really  composed 
of  several  colors,  and  that  bodies  reflect  only  the  rays  of 
their  own  colors,  while  they  absorb  all  the  other  rays. 

646.  Light  moves  with  the  amazing  rapidity  of  about 
95  millions  of  miles  in  8£  minutes,  since  it  is  proved  by 
certain  astronomical  observations,  that  the  light  of  the  SUD 
comes  to  the  earth  in  that  time.     This  velocity  is  so  great, 
that  to  any  distance  at  which  an  artificial  light  can  be  seen, 
it  seems  to  be  transmitted  instantaneously. 

If  a  ton  of  gunpowder  were  exploded  on  the  top  of  a 
mountain,  where  its  light  could  be  seen  a  hundred  miles, 
no  perceptible  difference  would  be  observed  in  the  time  of 
its  appearance  on  the  spot,  and  at  the  distance  of  a  hundred 
miles. 

REFRACTION  OF  LIGHT. 

647.  Although   a  ray  of  light  will   always  pass  in  a 
straight  line,  when  not  interrupted,  yet  when  it  passes  ob- 
liquely from  one  transparent  body  into  another,  of  a  differ- 
ent density,  it  leaves  its  linear  direction,  and  is  bent,  or  re- 
fracted, more  or  less,  out  of  its  former  course.  This  change 
in  the  direction  of  light,  seems  to  arise  from  a  certain  pow- 
er, or  quality,  which  transparent  bodies  possess  in  different 
degrees  ;  for  some  substances  bend  the  rays  of  light  much 
more  obliquely  than  others. 

The  manner  in  which  the  rays  of     A        Fig.  131. 
light  are  refracted,  may  be  readily 
understood  by  fig.   131. 

Let  a  be  a  ray  of  the  sun's  light, 
proceeding  obliquely  towards  the  sur- 
face of  the  water  c,  d,  and  let  e  be 
the  point  which  it  would  strike,  if 
moving  only  through  the  air.  Now, 
instead  of  passing  through  the  water 
in  the  line  a,  e,  it  will  be  bent  or  re- 
fracted, on  entering  the  water,  from  ,0  to  n,  and  having 
passed  through  the  fluid  it  is  again  refracted  in  a  contrary 

What  is  the  rate  of  velocity  with  which  light  moves'?  Can  we 
perceive  any  difference  in  the  time  which  it  takes  an  artificial  light  to 
j)ass  to  us  from  a  great  or  small  distance  7  What  is  meant  by  the  re- 
fraction of  light1?  Do  all  transparent  bodies  refract  light  equally  1  Ex- 
plain fig.  131,  and  show  how  the  ray  is  refracted  in  passing  into  anc 
out  of  the  water. 


OPTICS.  173 

direction  on  passing  out  of  the  water,  and  then  proceeds 
onward  in  a  straight  line  as  before. 

648.  The  refraction  of  water  is  beautifully  proved  by  the 
following  simple  experiment.  Place  an  empty  cup,  fig.  132, 
with  a  shilling  on  the  bottom,  in  such  a  position,  that  the 
side  of  the  cup  will  just  hide  the  piece  of  money  from  the 
eye.     Then  let  another  per-^x  FlS- 

son  fill  the  cup  with  v/ater,^ 
keeping  the  eye  in  the  same 
position  as  before.  As  the 
water  is  poured  in,  the  shil- 
ling will  become  visible,  ap- 
pearing to  rise  with  the  wa- 
ter. The  effect  of  the  water 
is  to  bend  the  ray  of  light 
coming  from  the  shilling,  so 

as  to  make  it  meet  the  eye  e 

below  the  point  where  it  otherwise  would.  Thus  the  eye 
could  not  see  the  shilling  in  the  direction  of  c,  since  the  line 
of  vision  is  towards  a,  and  c  is  hidden  by  the  side  of  the 
cup.  But  the  refraction  of  the  water  bends  the  ray  down 
wards,  producing  the  same  effect  as  though  the  object  had 
been  raised  upwards,  and  hence  it  becomes  visible. 

649.  The   transparent   body   through  which   the    light 
passes  is  called  the  medium,  and  it  is  found  in  all  cases, 
"  that  where  a  ray  of  light  passes  obliquely  from  one  medium 
into  another  of  a  different  density,  it  is  refracted,  or  turned 
out  of  its  former  course"     This  is  illustrated  in  the  above 
pxamples,  the  water  being  a  more  dense  medium  than  air. 
The  refraction  takes  place  at  the  surface  of  the  medium, 
and  the  ray  is  refracted  in  its  passage  out  of  the  refracting 
substance  as  well  as  into  it. 

650.  If  the  ray,  after  having  passed  through  the  water, 
then  strikes  upon  a  still  more  dense  medium,  as  a  pane  of 
glass,  it  will  again  be  refracted.     It  is  understood,  that  in 
all  cases  the  ray  must  fall  upon  the  refracting  medium  ob- 
liquely, in  order  to  be  refracted,  for  if  it  proceeds  from  one 
medium  to  another  perpendicularly  to  their  surfaces,  it  will 
pass  straight  through  them  all,  and  no  refraction  will  take 
place. 

Explain  fig.  132,  and  state  the  reason  why  the  shilling  seems  to  be 
raised  up  by  pouring  in  the  water.     What  is  a  medium  1     In  what 
direction  must  a  ray  of  light  pass  towards  the  medium  to  be  refracted  1 
Will  a  ray  falling:  perpendicularly  on  a  medium  be  refracted? 
15 


174 


OPTICS. 


Thus,  in  fig.  133,  let  a  represent  air,  b  Pig- 133. 
water,  and  c  a  piece  of  glass.  The  ray  d, 
striking  each  medium  in  a  perpendicular  di- 
rection, passes  through  them  all  in  a  straight 
line.  The  oblique  ray  passes  through  the 
air  in  the  direction  of  c,  but  meeting  the 
water,  is  refracted  in  the  direction  of  o  ;  then 
falling  upon  the  glass,  it  is  again  refracted 
in  the  direction  of  p,  nearly  parallel  with  the 
perpendicular  line  d. 

651.  In  all  cases  where  the  ray  passes  out 
of  a  rarer  into  a  denser  medium,  it  is  re- 
fracted towards  a  perpendicular  line,  raised 

from  the  surface  of  the  denser  medium,  and  P  ° 

so,  when  it  passes  out  of  a  denser,  into  a 

rarer  medium,  it  is  refracted  from  the  same  perpendicular. 

Let  the  medium  b,  fig.  134,  be  glass,  and  the  medium  ct 
water.    The  ray  a,  as  it  falls  upon  the  medium  b,  is  refract- 
ed towards  the  perpendicular  line  e,  d;  Fig.  134. 
but  when  it  enters  the  water,  whose  re- 
fractive power  is  less  than  that  of  glass, 
it  is  not  bent  so  near  the  perpendicular 
as  before,  and  hence  it  is  refracted  from, 
instead   of  towards,   the   perpendicular 
line,  and  approaches  the  original  direc- 
tion  of  the    ray   a,   g,   when    passing 
through  the  air. 

The  cause  of  refraction  appears  to  be 
the  power  of  attraction,  which  the  denser 
medium  exerts  on  the  passing  ray ;  and  in  all  cases  the  at- 
tracting force  acts  in  the  direction  of  a  perpendicular  to  the 
refracting  surface. 

652.  The  refraction  of  the  rays  of  light,  as  they  fall  upon 
the  surface  of  the  water,  is  the  reason  why  a  straight   rod, 
with  one  end  in  the  water,  and  the  other  end  rising  above 
it,  appears  to  be  broken,  or  bent,  and  also  to  be  shortened. 

Suppose  the  rod  a,  fig.  135,  to  be  set  with  one  half  of  its 
length  below  the  surface  of  the  water,  and  the  other  half 
above  it.  The  eye  being  placed  in  an  oblique  direction, 

Explain  fig.  133,  and  show  how  the  ray  e  is  refracted.  When  the 
ray  passes  out  of  a  rarer  into  a  denser  medium,  in  what  direction  is  it 
refracted?  When  it  passes  out  of  a  denser  into  a  rarer  medium,  in 
what  direction  is  the  refraction  7  Explain  this  by  fig.  134.  What  i* 
the  cause  of  refraction  7  What  is  the  reason  that  a  rod,  with  one  end 
in  the  water,  appears  distorted  and  snorter  than  it  really  is  7 


OPTICS.  175 

will  see  the  lower  end  apparently  at  the  point  o,  while  the 
real  termination  of  the  rod  would  be  at  n:  Fig.  135. 
the  refraction  will  therefore  make  the  rod 
appear  shorter  by  the  distance  from  o  to 
n,  or  one  fourth  shorter  than  the  part  be- 
low the  water  really  is.  The  reason  why. 
the  rod  appears  distorted,  or  broken,  is, 
that  we  judge  of  the  direction  of  the  part 
which  is  under  the  water,  by  that  which! 
is  above  it,  and  the  refraction  of  the  rays  coming  from  below 
the  surface  of  the  water,  give  them  a  different  direction,  when 
compared  with  those  coming  from  that  part  of  the  rod  which 
is  above  it.  Hence,  when  the  whole  rod  is  below  the  water, 
no  such  distorted  appearance  is  observed,  because  then  all 
the  rays  are  refracted  equally. 

For  the  reason  just  explained,  persons  are  often  deceived 
in  respect  to  the  depth  of  water,  the  refraction  making  it 
appear  much  more  shallow  than  it  really  is;  and  there  is 
no  doubt  but  the  most  serious  accidents  have  often  happen- 
ed to  those  who  have  gone  into  the  water  under  such  decep- 
tion ;  for  a  pond  which  is  really  six  feet  deep,  will  appear  to 
the  eye  only  a  little  more  than  four  feet  deep. 

REFLECTION  OF  LIGHT. 

653.  If  a  boy  throws  his  ball  against  the  side  of  a  house 
swiftly,  and  in  a  perpendicular  direction,  it  will  bound  back 
nearly  in  the  line  in  which  it  was  thrown,  and  he  will  be  able 
to  catch  it  with  his  hands ;  but  if  the  ball  be  thrown  oblique- 
ly to  the  right,  or  left,  it  will  bound  away  from  the  side  of  the 
house  in  the  same  relative  direction  in  which  it  was  thrown. 

The  reflection  of  light,  so  far  as  re-          Fig.  136. 
gards  the  line  of  approach,  and  the  line    c 
of  leaving  a  reflecting  surface,  is  gov- 
erned by  the  same  law. 

Thus,  if  a  sun  beam,  fig.  136,  passing 
through  a  small  aperture  in  the  window 
shutter  a,  be  permitted  to  fall  upon  the 
plane  mirror,  or  looking  glass,  c,  d,  at 
right  angles,  it  will  be  reflected  back  at  right  angles  with 
the  mirror,  and  therefore  will  pass  back  again  in  exactly 
the  same  direction  in  which  it  approached. 

Why  does  the  water  in  a  pond  appear  less  deep  than  it  really  is  ? 
Suppose  a  sun  beam  fall  upon  a  plane  mirror,  at  right  angles  with  its 
surface,  in  what  direction  will  it  be  reflected? 


176 


MIRRORS. 


654.  But  if  the  ray  strikes  the  mirror  in  an  oblique  di 
rection,  it  will  also  be  thrown  off  in  an          Fig.  137. 
oblique   direction,   opposite    to    that    in 

which  it  was  thrown. 

Let  a  ray  pass  towards  a  mirror  in  the 
line  a,  c,  fig.  137,  it  will  be  reflected  off 
in  the  direction  of  c,  d,  making  the  an-  c 
gles  1  and  2  exactly  equal. 

The  ray  a,  c,  is  called  the  inci&tnt 
ray,  and  the  ray  c,  d,  the  reflected  ray  j 
and  it  is  found,  in  all  cases,  that  whatever 
angle  the  ray  of  incidence  makes  with  the  reflecting  sur- 
face, or  with  a  perpendicular  line  drawn  from       p-     j^g 
the  reflecting  surface,  exactly  the  same  angle 
is  made  by  the  reflected  ray. 

655.  From  these  facts,  arise  the  general 
law  in  optics,  that  the  angle  of  reflection  is 
equal  to  the  angle  of  incidence. 

The  ray  a,  c,  fig.  138,  is  the  ray  of  inci-^j 
dence,  and  that  from  c  to  d,  is  the  ray  of  re- 
flection. The  angles  which  a,  c,  make  with 
the  perpendicular  line,  and  with  the  plane  of 
the  mirror,  is  exactly  equal  to  those  made  by 
c,  d,  with  the  same  perpendicular,  and  the 
same  plane  surface. 

MIRRORS. 

656.  Mirrors  are  of  three  kinds,  namely,  plane,  convex, 
and  concave.     They  are  made  of  polished   metal,  or  of 
glass  covered  on  the  back  with  an  amalgam  of  tin  and 
quicksilver. 

The  common  looking  glass  is  a  plane  mirror,  and  con- 
sists of  a  plate  of  ground  glass  so  highly  polished  as  to  per- 
mit the  rays  of  light  to  pass  through  it  with  little  interrup- 
tion. On  the  back  of  this  plate  is  placed  the  reflecting  sur- 
face, which  consists  of  a  mixture  of  tin  and  mercury.  The 
glass  plate,  therefore,  only  answers  the  purpose  of  sustain- 
ing the  metallic  surface  in  its  place, — of  admitting  the  rays 

Suppose  the  ray  falls  obliquely  on  its  surface,  in  what  direction  will 
it  then  be  reflected  1  What  is  an  incident  ray  of  light  ?  What  is  a 
reflected  ray  of  light  ?  What  general  law  in  optics  results  from  ob- 
servations on  the  incident  and  reflected  rays  ?  How  many  kinds  of 
mirrors  are  there  1  What  kind  of  mirror  is  the  common  looking  glass  I 
Of  what  use  is  the  glass  plate  in  the  construction  of  this  mirror  7 


MIRRORS.  177 

of  light  to  and  from  it,  and  of  preventing  its  surface  from 
tarnishing,  by  excluding  the  air.  Could  the  metallic 
surface,  however,  be  retained  in  its  place,  and  not  exposed 
to  the  air,  without  the  glass  plate,  these  mirrors  would  be 
much  more  perfect  than  they  are,  since,  in  practice,  glass 
cannot  be  made  so  perfect  as  to  transmit  all  the  rays  of  light 
which  fall  on  its  surface. 

657.  When  applied  to  the  plane  mirror,  the  angles  of  in- 
cidence and  of  reflection  are  equal,  as  already  stated ;  and  it 
therefore  follows,  that  when  the  rays  of  light  fall  upon  it 
obliquely  in  one  direction,  they  are  thrown  off  under  the 
same  angle  in  the  opposite  direction. 

This  is  the  reason  why  the  images  of  objects  can  be  seen 
when  the  objects  themselves  are  not  visible. 

Suppose  the  mirror  a  b,  fig.  139,  to  Fig.  139. 

be  placed  on  the  side  of  a  room,  and  a 
lamp  to  be  set  in  another  room,  but  so 
situated,  as  that  its  light  would  shine 
upon  the  glass.  The  lamp  itself  could 
not  be  seen  by  the  eye  placed  at  e,  be- 
cause the  partition  d  is  between  them ; 
but  its  image  would  be  visible  at  e,  be- 
cause the  angle  of  the  incident  ray, 
coming  from  the  light,  and  that  of  the 
reflected  ray  which  reaches  the  eye, 
are  equal. 

658.  An  image  from  a  plane  mir- 
ror appears  to  be  just  as  far  behind  the  mirror  as  the  object 
is  before  it,  so  that  when  a  person  approaches  this  mirror, 
his  image  seems  to  come  forward  to  meet  him ;  and  when 
he  withdraws  from  it,  his  image  appears  to  be  moving  back- 
ward at  the  same  rate.     For  the  same  reason,  the  different 
parts  of  the  same  object  will  appear  to  extend  as  far  behind 
the  mirror,  as  they  are  before  it. 

If,  for  instance,  one  end  of  a  rod,  two  feet  long,  be  made 
to  touch  the  surface  of  such  a  mirror,  this  end  of  the  rod, 
and  its  image,  will  seem  nearly  to  touch  each  other,  there 
being  only  the  thickness  of  the  glass  between  them  ;  while 
the  other  end  of  the  rod,  and  the  other  end  of  its  image,  will 
appear  to  be  equally  distant  from  the  point  of  contact. 

Explain  fig.  139,  and  show  how  the  image  of  an  object  can  be  seen 
in  a  plane  mirror,  when  the  real  object  is  invisible.  "The  image  of  an 
object  appears  just  as  far  behind  a  plane  mirror,  as  the  object  is  before 
it;  explain  fig.  140,  and  show  why  this  is  the  case. 


178  MIRRORS. 

The  reason  of  this  is  explained  on  the  principle,  that  the 
angle  of  incidence  and  that  of  reflection  is  equal. 

Suppose  the  arrow  a,  to  he  the  object  reflected  by  the 
mirror  d  c,  fig.  140;  the  inci-  Fig.  140. 

dent  rays  a,  flowing  from  the 
end  of  the  arrow,  being  thrown 
back  by  reflection,  will  meet 
the  eye  in  the  same  state  of  di- 
vergence that  they  would  do>(£ 
if  they  proceeded  to  the  same 
distance  behind  the  mirror,  that 
the  eye  is  before  it,  as  at  o. 
Therefore,  by  the  same  law, 
the  reflected  rays,  where  they 
meet  the  eye  at  e,  appear  to  di- 
verge from  a  point  A,  just  as  far  behind  the  mirror,  as  a  is 
before  it,  and  consequently  the  end  of  the  arrow  most  re- 
mote from  the  glass,  will  appear  to  be  at  A,  or  the  point 
where  the  approaching  rays  would  meet,  were  they  contin- 
ued onward  behind  the  glass.  The  rays  flowing  from  every 
other  part  of  the  arrow  follow  the  same  law;  and  thus  every 
part  of  the  image  seems  to  be  at  the  same  distance  behind 
the  mirror,  that  the  object  really  is  before  it. 

659.  In  a  plane  mirror,  a  person  may  see  his  whole  im- 
age, when  the  mirror  is  only  half  as  long  as  himself;  let 
him  stand  at  any  distance  from  it  whatever. 

This  is  also  explained  by  the  law,  that  the  angles  of  in- 
cidence and  reflection  are  equal.  If  the  mirror  be  elevated, 
so  that  the  ray  of  light  from  the  eye  falls  perpendicularly 
upon  the  mirror,  this  ray  will  be  thrown  back  by  reflection 
in  the  same  direction,  so  that  the  incident  and  reflected  ray 
by  which  the  image  of  the  eyes  and  face  are  formed,  will 
be  nearly  parallel,  while  the  ray  flowing  from  his  feet  will 
fall  on  the  mirror  obliquely,  and  will  be  reflected  as  ob- 
liquely in  the  contrary  direction,  and  so  of  all  the  other  rays 
by  which  the  image  of  the  different  parts  of  the  person  is 
formed. 

Thus,  suppose  the  mirror  c  e,  fig.  141,  to  be  just  half  as 
long  as  the  arrow  placed  before  it,  and  suppose  the  eye  to  be 
placed  at  a.  Then  the  ray  a  e,  proceeding  from  the  eye  at 


What  must  be  the  comparative  length  of  a  plane  mirror,  in  which 
a  person  may  see  his  whole  image*?  In  what  part  of  the  image,  fig. 
141,  are  the  incidental  and  reflected  rays  nearly  parallel? 


MIRRORS. 


179 


a,  and  falling  perpen-  Fig.  141. 

dicularly  on  the  glass 
at  c,  wilL  be  reflected 
back  to  the  eye  in  the 
same  line,  and  this  part 
of  the  image  will  ap- 
pear at  b,  in  the  same 
line,  and  at  the  same 
distance  behind  the 
glass,  that  the  arrow  is 
before  it.  But  the  ray 
flowing  from  the  lower 

extremity  of  the  arrow,  will  fall  on  the  mirror  obliquely,  as 
at  e,  and  will  be  reflected  under  the  same  angle  to  the  eye, 
and  therefore  the  extremity  of  the  image,  appearing  in  the 
direction  of  the  reflected  ray,  will  be  seen  at  d.  The  rays 
flowing  from  the  other  parts  of  the  arrow,  will  observe  the 
same  law,  and  thus  the  whole  image  is  seen  distinctly,  and 
in  the  same  position  as  the  object. 

To  render  this  still  more  obvious,  suppose  the  mirror  to 
be  removed,  and  another  arrow  to  be  placed  in  the  position 
where  its  image  appears,  behind  the  mirror,  of  the  same 
length  as  the  one  before  it.  Then  the  eye,  being  in  the 
same  position  as  represented  in  the  figure,  would  see  the 
different  parts  of  the  real  arrow  in  the  same  direction  that 
it  before  saw  the  image.  Thus,  the  ray  flowing  from  the 
upper  extremity  of  the  arrow,  would  meet  the  eye  in  the 


direction  of  b  c,  while  the  ray, 
coming  from  the  lower  extremity, 
would  fall  on  it  in  the  direction 
of  e  d. 

660.  CONVEX  MIRROR. — A 
convex  mirror  is  a  part  of  a 
sphere,  or  globe,  reflecting  from 
the  outside. 

Suppose  fig.  1 42  to  be  a  sphere, 
then  the  part  from  a  to  o,  would 
be  a  section  of  the  sphere.  Any 
part  of  a  hollow  ball  of  glass, 


Fig.  142. 


— c 


Why  does  the  image  of  the  lower  part  of  the  arrow  appear  at  d  ? 
Suppose  the  mirror,  fig.  141,  to  be  removed,  and  an  arrow  of  the  same 
length  to  be  placed  where  the  image  appeared,  would  the  direction  of 
the  rays  from  the  arrow  be  the  same  that  they  were  from  the  image  ? 
W  hat  is  a  convex  mirror  ? 


180 


MIRRORS. 


Fig.  143. 


%vith  an  amalgam  of  tin  and  quicksilver  spread  on  the  in- 
side, or  any  part  of  a  metallic  globe  polished  on  the  outside, 
would  form  a  convex  mirror. 

The  axis  of  a  convex  mirror,  is 
a  line,  as  c  b,  passing  through  its 
centre. 

661.  Rays  of  light  are  said   to 
diverge,  when  they  proceed  from 
the  same  point,  and  constantly 
cede  from  each  other,  as  from  the 
point  a,  fig.  143.    Rays  of  light  are 

said  to  converg&^-when.  they  approach  each  other  in  such 
u  direction  as  finally  to  meet  at  a  point,  as  at  b,  fig.  143. 

The  image  formed  by  a  plane  mirror,  as  we  have  al- 
ready seen,  is  of  the  same  size  as  the  object,  but  the  image 
reflected  from  the  convex  mirror  is  always  smaller  than  cne 
object. 

The  law  which  governs  the  passage  of  light  with  respect 
to  the  angles  of  incidence  and  reflection,  to  and  from  the 
convex  mirror,  is  the  same  as  already  stated,  for  the  plane 
mirror. 

662.  From  the  surface  of  a  plane  mirror,  parallel  rays 
are  reflected  parallel ;  but  the  convex  mirror  causes  parallel 
rays  falling  on  its  surface  to  diverge,  by  reflection. 

To   make   this  understood,  Fig.  144. 

let  1,  2,  3,  fig.  144,  be  parallel 
rays,  falling  on  the  surface  of 
the  convex  reflector,  of  which 
a  would  be  the  centre,  were  the 
reflector  a  whole  sphere.  The 
ray  2  is  perpendicular  to 
the  surface  of  the  mirror,  for 
when  continued  in  the  same 
direction,  it  strikes  the  axis,  or 
centre  of  the  circle  a.  The  two 
rays,  1  and  3,  being  parallel 
to  this,  all  three  would  fall  on 
a  plane  mirror  in  a  perpendi- 
cular direction,  and  conse- 
quently would  be  reflected  in  the  lines  of  their  incidence. 

What  is  the  axis  of  a  convex  mirror  1  What  are  diverging  rays  7 
What  are  converging  rays  1  What  law  governs  the  passage  of  light 
from  and  to  the  convex  mirror  ?  Are  parallel  rays  falling  on  a  con. 
vex  mirror,  reflected  parallel?  Explain  fig.  144. 


MIRRORS.  1P1 

But  the  obliquity  of  the  convex  surface,  it  is  obvious,  will 
lender  the  direction  of  the  rays  1  and  3,  oblique  to  that  sur- 
face, for  the  same  reason  that  2  is  perpendicular  to  that  part 
of  the  circle  on  which  it  falls.  Rays  falling  on  any  part 
of  this  mirror,  in  a  direction  which,  if  continued  through 
the  circumference,  would  strike  the  centre,  are  perpendicu- 
lar to  the  side  where  they  fall.  Thus,  the  dotted  lines,  c  a, 
and  d  a,  are  perpendicular  to  the  surface,  as  well  as  2. 

Now  the  reflection  of  the  ray  2,  will  be  back  in  the  line 
of  its  incidence,  but  the  rays  1  and  3,  falling  obliquely,  are 
reflected  under  the  same  angles  at  which  thoy  fall,  and  there- 
fore their  lines  of  reflection  will  be  as  far  without  the  per- 
pendicular lines  c  a,  and  d  a,  as  the  lines  of  their  incident 
rays,  1  and  3,  are  within  them,  and  consequently  they  will 
diverge  in  the  direction  of  e  and  o ;  and  since  we  always  see 
the  image  in  the  direction  of  the  reflected  ray,  an  object 
placed  at  1,  would  appear  behind  the  surface  of  the  mirror 
at  n,  or  in  the  direction  of  the  line  o  n. 

663.  Perhaps  the  subject  of  the  convex  mirror  will  be 
better  understood,  by  considering  its  surface  to  be  formed  of 
a  number  of  plane  surfaces,  indefinitely  small.  In  this  case, 
each  point  from  which  a  ray  is  reflected,  would  act  in  the 
same  manner  as  a  plane  mirror,  and  the  whole,  in  the  man- 
ner of  a  number  of  minute  mirrors  inclined  from  each 
other. 

Suppose  a  and  b,  fig.  145,  to 
be  the  points  on  a  convex  mir- 
ror, from  which  the  two  parallel 
rays,  c  and  d,  are  reflected.  Now, 
from  the  surface  of  a  plane  mir- 
ror, the  reflected  rays  would  be 
parallel,  whenever  the  incident 
ones  are  so,  because  each  will 
fall  upon  the  surface  under  the 
same  angles.  But  it  is  obvious, 
in  the  present  case,  that  these 
rays  fall  upon  the  surfaces,  a>  and  b,  under  different  angles, 
as  respects  the  surfaces,  c  approaching  in  a  more  oblique 
direction  than  d ;  consequently  c  is  reflected  more  otliquelv 
than  d,  and  the  two  reflected  rays,  instead  of  being  parallel, 
ns  before,  diverge  in  the  direction  of  n  and  o. 


How  is  the  action  of  the  convex  mirror  illustrated  by  a  number  of 
plane  mirrors  7 

16 


182  MIRRORS. 

664.  Again,  the  two  con-  .       Fig.  146. 
verging   rays   a  and   b,   fig. 

146,  without  the  interposition 
of  the  reflecting  surfaces,  ^ 
would  meet  at  c}  but  because 
the  angles  of  reflection  are 
equal  to  those  of  incidence, 
and  because  the  surfaces  of 
reflection  are  inclined  to  each 
other,  these  -ays  are  reflected 
less  converge!  t,  and  instead 
of  meeting  at  the  same  dis- 
tance before  the  mirror  that 

c  is  behind  it,  are  sent  off  in  the  direction  of  e,  at  which 
point  they  meet. 

665.  "  Thus  parallel  rays  falling  on  a  convex  mirror, 
are  rendered  diverging  by  reflection ;  converging  rays  are 
made  less  convergent,  or  parallel,  and  diverging  rays  more 
divergent." 

The  effect  of  the  convex  mirror,  therefore,  is  to  disperse 
the  rays  of  light  in  all  directions ;  and  it  is  proper  here  to 
remind  the  pupil,  that  although  the  rays  of  light  are  repre- 
sented on  paper  by  single  lines,  there  are  in  fact  probably 
millions  of  rays,  proceeding  from  every  point  of  all  visible 
bodies.  Only  a  comparatively  small  number  of  these  rays, 
it  is  true,  can  enter  the  eye,  for  it  is  only  by  those  which 
proceed  in  straight  lines  from  the  different  parts  of  the  ob- 
ject, and  enter  the  pupil,  that  the  sense  of  vision  is  ex- 
sited. 

Now,  to  conceive  how  exceedingly  small  must  be  the 
proportion  of  light  thrown  off,  from  any  visible  object  which 
enters  the  eye,  we  must  consider  that  the  same  object  re- 
flects rays  in  every  other  direction,  as  well  as  in  that  in 
which  it  is  seen.  Thus,  the  gilded  ball  on  the  steeple  of  a 
church  may  be  seen  by  millions  of  persons  at  the  same  time, 
who  stand  upon  the  ground  ;  and  were  millions  more  raised 
above  these,  it  would  be  visible  to  all.  . 

When,  therefore,  it  is  said,  that  the  convex  mirror  dis- 


Explain  fig.  146  What  effect  does  the  convex  mirror  have  upon 
parallel  rays  by  reflection  1  What  is  its  effect  on  converging  rays  1 
What  is  its  eff^t  on  diverging  rays  1  Do  the  rays  of  light  proceed 
only  from  ther xtremities  of  objects,  as  represented  in  figures,  or  from 
all  their  parts  1  Do  all  the  rays  of  light  proceeding  from  an  object  en- 
ter the  eye,  or  only  a  few  of  them  ? 


MIRRORS.  183 

pei  es  the  rays  of  light  which  fall  upon  it  from  any  ob- 
ject, and  when  the  direction  of  these  reflected  rays  are- 
shown  only  by  single  lines,  it  must  be  remembered,  that 
each  line  represents  pencils  of  rays,  and  that  the  light  not 
only  flows  from  the  parts  of  the  object  thus  designated,  but 
from  all  the  other  parts.  Were  this  not  the  case,  the  object 
would  be  visible  only  at  certain  points. 

666.  The  images  of  objects  reflected  from  the  convex 
mirror,  appear  curved,  because  their  different  parts  are  not 
equally  distant  from  its  surface. 

If  the  object  a  be  placed  Fig.  147. 

obliquely  before  the  convex 
mirror,  fig.  147,  then  the  con- 
verging rays  from  its  two  ex- 
tremities falling  obliquely  on 
its  surface,  would,  were  they 
prolonged  through  the  mir- 
ror, meet  at  the  point  c, 
hind  it.  But  instead  of  be- 
ing  thus  continued,  they  are 
thrown  back  by  the  mirror, 

in  less  convergent  lines,  which  meet  the  eye  at  c,  it  being, 
ns  we  have  seen,  one  of  the  properties  of  this  mirror,  to  re- 
flect converging  rays  less  convergent  than  before. 

The  image  being  always  seen  in  the  direction  from  which 
'.he  rays  approach  the  eye,  it  appears  behind  the  mirror  at 
d.  If  the  eye  be  kept  in  the  same  position,  and  the  object, 
a,  be  moved  further  from  the  mirror,  its  image  will  appear 
smaller,  in  a  proportion  inversely  to  the  distance  to  which 
it  is  removed.  Consequently,  by  the  same  law,  the  two 
ends  of  a  straight  object  will  appear  smaller  than  its  mid- 
dle, because  they  are  further  from  the  reflecting  surface  of 
the  mirror.  Thus,  the  images  of  straight  objects,  held  be- 
fore o  convex  mirror,  appear  curved,  and  for  the  same  rea- 
son, the  features  of  the  face  appear  out  of  proportion,  the 
nose  being  too  large,  and  the  cheeks  too  small,  or  narrow. 

The  reason  why  the  image  appears  less  than  the  object  is, 
that  the  convex  surface  of  the  mirror  has  the  property,  as 

What  would  be  the  consequence,  if  the  rays  of  light  proceeded  only 
from  the  parts  of  an  object  shown  in  diagrams  7  Why  do  the  images 
of  objects  "effected  from  convex  mirrors  appear  curved  1  Why  do  the 
features  of  the  face  appear  out  of  proportion,  by  this  mirror  f  Why 
^oes  an  -.  <i^e  reflected  from  a  convex  surface  appear  smaller  than  the 
' 


184  MIRRORS. 

stated  above,  of  decreasing  the  convergency  of  the  incidental 
rays  by  reflection. 

667.  Now,  objects  appear  to  us  large  or  small,  in  propor- 
tion to  the  angle  which  the  rays  of  light,  proceeding  from 
their  extreme  parts,  form,  when  they  meet  at  the  eye.     For 
it  is  plain  that  the  half  of  any  object  will  appear  under  a 
less  angle  than  the  whole,  and  the  quarter  under  a  less  angle 
still.  Therefore  the  smaller  an  object  is,  the  smaller  will  be 
the  angle  under  which  it  will  appear  at  a  given  distance.  If 
then  a  mirror  makes  the  angle  under  which  an  object  is 
seen  smaller,  the  object  itself  will  seem  smaller  than  it  really 
is.     Hence  the  image  of  an  object,  when  reflected  from  the 
convex  mirror,  appears  smaller  than  the  object  itself.     This 
will  be  understood  by  fig.  148. 

Suppose  the  rays  flow-  Fig.  148. 

ing  from  the  extremities  of 
the  object  a,  to  be  reflect- 
ed back  to  c,  under  the 
same  degrees  of  conver- 
gence at  which  they  strike 
the  mirror ;  then,  as  in  the 
plane  mirror,  the  image  d, 
would  appear  of  the  same 
size  as  the  object  a;  for  f 
if  the  rays  from  a  were^f 
prolonged  behind  the  mirror,  they  would  meet  at  b,  but 
forming  the  same  angle,  by  reflection,  that  they  would  do, 
if  thus  prolonged,  the  object  seen  from  bt  and  its  image  from 
c,  would  appear  of  the  same  dimensions. 

But  instead  of  this,  the  rays  from. the  arrow  a,  being  ren- 
dered less  convergent  by  reflection,  are  continued  onward, 
and  meet  the  eye  under  a  more  acute  angle  than  at  c,  the 
angle  under  which  they  actually  meet,  being  represented  at 
e,  consequently  the  image  of  the  object  is  shortened  in  pro- 
portion to  the  acuteness  of  this  angle,  and  the  object  ap- 
pears diminished,  as  represented  at  o. 

668.  The  image  of  an  object,  as  already  stated,  appears 
less  as  the  object  is  removed  to  a  greater  distance  from  the 
mirror. 

Why  does  the  half  of  an  object  appear  to  the  eye  smaller  than  the 
whole  1  Suppose  the  angles  c  and  0,  fig.  148,  are  equal,  will  there 
be  any  difference  between  the  size  of  the  object  and  its  image  1  How  is 
the  image  affected,  when  the  object  is  withdrawn  from  the  surface  of  a 
convex  mirror  1 


MIRRORS.  185 

To  exj  fain  the  reason  of  this,  Fig.  149. 

let  us  su]  pose  that  the  arrow  a, 
fig.  149,  \6  diminished  by  reflec- 
tion from  the  convex  surface,  so 
that  its  image  appearing  at  d, 
with  the  eye  at  c,  shall  seem  as 
much  smaller  in  proportion  to  the 
object,  as  d  is  less  than  a.  Now, 
keeping  the  eye  at  the  same 
tance  from  the  mirror,  withdraw 
the  object,  so  that  it  shall  be  equally  distant  with  the  eye, 
ind  the  image  will  gradually  diminish,  as  the  arrow  is  re- 
moved. 

669.  The  reason  of  this  will  be  Fig.  150. 
made  plain  by  the  next  figure ; 

for  as  the  arrow  is  moved  back- 
wards, the  angle  at  c,  fig.  150, 
must  be  diminished,  because  the 
rays  flowing  from  the  extremi- 
ties of  the  object  fall  a  greater 
distance  before  they  reach  the  sur- 
face of  the  mirror ;  and  as  the 
angles  of  the  reflected  rays  bear 
a  proportion  to  those  of  the  incident  ones,  so  the  angle  of 
vision  will  become  less  in  proportion  as  the  object  is  with- 
drawn. The  effect  therefore  of  withdrawing  the  object,  is 
first  to  lessen  the  distance  between  the  converging  rays,  flow- 
ing from  it,  at  the  point  where  they  strike  the  mirror,  and 
as  a  consequence  to  diminish  the  angle  under  which  the  re- 
flected rays  convey  its  image  to  the  eye. 

670.  In  the  plane  mirror,  as  already  shown,  the  image 
appears  exactly  as  far  behind  the  mirror  as  the  object  is 
before  it,  ^at  the  convex  mirror  shows  the  image  just  under 
the  surface,  or,  when  the  object  is  removed  to  a  distance,  a 
little  way  behind  it.     To  understand  the  reason  of  this  dif- 
ference, it  must  be  remembered,  that  the  plane  mirror  makes 
the  image  seem  as  far  behind  as  the  object  is  before  it,  because 
the  rays  are  reflected  in  the  same  relative  position,  at  which 
they  fall  upon  its  surface.     Thus,  parallel  rays  are  reflected 

Explain  figures  149  and  150,  and  show  the  reason  why  the  images 
are  diminished  when  the  objects  are  removed  from  the  convex  mirror. 
What  is  said  to  be  the  first  effect  of  withdrawing  the  object  from  a 
concave  surface,  and  what  the  consequence  on  the  angle  of  reflected 
rays? 

16* 


186  MIRRORS. 

parallel;  divergent  rays  equally  divergent,  and  converger* 
rays  equally  convergent.  But  the  convex  mirror,  as  also 
above  shown,  reflects  convergent  rays  less  convergent,  and 
divergent  rays  more  divergent,  and  it  is  from  this  property 
of  the  convex  mirror  that  the  image  appears  near  its  sur- 
face, and  not  as  far  behind  it  as  the  object  is  before  it,  as  in 
the  plane  mirror. 

Let  us  suppose  that  a,  fig.  151,  is  a  Fig.  151. 

luminous  point,  from  which  a  pencil 
of  diverging  rays  fall  upon  a  convex 
mirror.  These  rays,  as  already  de- 
monstrated,  will  be  reflected  more  di- 
vergent, and  consequently  will  meet 
the  eye  at  e,  in  a  wider  state  of  disper- 
sion than  they  fell  upon  the  mirror  at  o. 
Now,  as  the  image  will  appear  at  the 
point  where  the  diverging  rays  would 
converge  to  a  focus  in  a  contrary  direction,  were  they  pro- 
longed behind  the  mirror,  so  it  cannot  appear  as  far  behind 
the  reflecting  surface  as  the  object  is  before  it,  for  the  more 
widely  the  rays  meeting  at  the  eye  are  separated,  the  shorter 
will  be  the  distance  at  which  they  will  come  to  a  point. 
The  image  will,  therefore,  appear  at  n,  instead  of  appearing 
at  an  equal  distance  behind  the  mirror  that  the  object  a  is 
before  it. 

671.  CONCAVE  MIRROR. — The  shape  of  the  concave 
mirror  is  exactly  like  that  of  the  convex  mirror,  the  only 
difference  between  them  being  in  respect  to  their  reflecting 
surfaces.  The  reflection  of  the  concave  mirror  takes  place 
from  its  inside,  or  concave  surface,  while  that  of  the  convex 
mirror  is  from  the  outside,  or  convex  surface.  Thus  the 
section  of  a  metallic  sphere,  polished  on  both  si  1<3s,  is  both 
a  concave  and  convex  mirror,  as  one  or  the  othei  side  i» 
employed  for  reflection. 

The  effect  and  phenomena  of  this  mirror  will  therefore 
be,  in  many  respects,  directly  the  contrary  from  those  al- 
ready detailed,  in  reference  to  the  convex  mirror. 

From  the  plane  mirror,  the  relation  of  the  incident  rays 
are  not  changed  by  reflection  ;  from  the  convex  mirror  they 
are  dispersed ;  but  the  concave  mirror  renders  the  rays  re- 
Explain  the  reason  why  the  image  appears  near  the  surface  of  the 
convex  mirror.  What  is  the  shape  of  the  concave  mirror,  and  in  what 
respect  does  it  differ  from  the  convex  mirror  1  How  may  convex  and 
concave  mirrors  be  united  in  the  same  instrument  ? 


MIRRORS.  187 

Aected  from  it  more  convergent,  and  tends  to  concentrate 
them  into  a  focus. 

The  surface  of  the  concave  mirror,  like  that  of  the  con- 
vex, may  be  considered  as  a  great  number  of  minute  plane 
mirrors,  inclined  to  each  other  at  certain  angles,  in  propor- 
tion to  its  concavity. 

672.  The  laws  of  incidence  and  reflection  are  the  same, 
when  applied  to  the  concave  mirror,  as  those  already  ex- 
plained in  reference  to  the  other  mirrors. 

In  reference  to  the  concave  mirror,  Fig.  152. 

let  us,  in  the  first  place,  examine  the  ef- 
fect of  two  plane  mirrors  inclined  to  c 
each  other,  as  in  fig.  152,  on  parallel 
rays  of  light.  The  incident  rays,  a  and 
b,  being  parallel  before  they  reach  the 
reflectors,  are  thrown  off  at  unequal  an- 
gles in  respect  to  each  other,  for  b  falls 
on  the  mirror  more  obliquely  than  a,  and 
consequently  is  thrown  off  more  oblique-  /  / 

iy  in  a  contrary  direction,  therefore,  the  '      ' 

angles  of  reflection  being  equal  to  those  of  incidence,  the 
two  rays  meet  at  c.  Thus  we  see  that  the  effect  of  two 
plane  mirrors  inclined  to  each  other,  is  to  make  parallel 
rays  converge  and  meet  in  a  focus. 

The  same  result  would  take  place,  whether  the  mirror 
was  one  continued  circle,  or  an  infinite  number  of  small 
mirrors  inclined  to  each  other  in  the  same  relation  as  the 
different  parts  of  the  circle. 

The  effect  of  this  mirror,  as  we  have  seen,  being  to  ren- 
der parallel  rays  convergent,  the  same  principle  will  render 
diverging  rays  parallel,  and  converging  rays  still  more  con- 
vergent. 

673.  The  focus  of  a  concave  mirror  is  the  point  where  the 
rays  are  brought  together  by  reflection.     The  centre  of  con- 
cavity in  a  concave  mirror,  is  the  centre  of  the  sphere,  of 
which  the  mirror  is  a  part.     In  all  concave  mirrors,  the  fo- 
cus of  parallel  rays,  or  rays  falling  directly  from  the  sun,  is 
at  the  distance  of  half  the  semi-diameter  of  the  sphere,  or 
globe,  of  which  the  reflector  is  a  part. 

Thus,  the  parallel  rays  1,  2,  3,  &c.,  fig.  153,  all  meet  at 

What  is  the  difference  of  effect  between  the  concave,  convex,  and 
plane  mirrors,  on  the  reflected  rays  1  In  what  respect  may  the  concave 
mirror  be  considered  as  a  number  of  plane  mirror?  a  What  is  the  fo- 
•us  of  a  concave  mirror  1 


i88 


MIRRORS. 


ihe  point  o,  which  is  half  the  distance  between  the  centre 
ft,  of  the  whole  sphere,  Fig.  153 

and  the  surface  of  the 

reflector,  and  therefore 
one  quarter  the  diame- 
ter of  the  whole  sphere, 
of  which  the  mirror  is 
a  part. 

674.  In  concave  mir- 
rors, of  all  dimensions, 
the  reflected  rays  fol- 
low the  same  law;  that 
is,  parallel  rays  meet 
and  cross  each  other  at 
the  .  distance  of  one 
fourth  the  diameter  of 

the  sphere  of  which  they  are  sections.     This  point  is  called 
the  principal  focus  of  the  reflector. 

But  if  the  incident  rays  are  divergent,  the  focus  will  be 
removed  to  a  greater  distance  from  the  surface  of  the  mir- 
ror, than  when  they  are  parallel,  in  proportion  to  their  di- 
vergency. 

This  might  be  inferred  from  the 
general  laws  of  incidence  and  reflec- 
tion, but  will  be  made  obvious  by  fig. 
154,  where  the  diverging  rays  1,  2,  3, 
4,  form  a  focus  at  the  point  0,  where- 
as, had  they  been  parallel,  their  focus 
would  have  been  at  a.  That  is,  the 
actual  focus  is  at  the  centre  of  the 
sphere,  instead  of  being  half  way  be- 
tween the  centre  and  circumference,  as 
is  the  case  when  the  incident  rays  are 
parallel.  The  real  focus,  therefore,  is  beyond,  or  without, 
the  principal  focus  of  the  mirror. 

675.  By  the  same  law,  converging  rays  will  form  a  point 
within  the  principal  focus  of  a  mirror. 

Thus,  were  the  rays  falling  on  the  mirror,  fig.  155,  par- 
allel, the  focus  would  be  at  a;  but  in  consequence  of  their 

At  what  distance  from  its  surface  is  the  focus  of  parallel  rays  in  this 
mirror  1  What  is  the  principal  focus  of  a  concave  mirror  1  If  th»,  in- 
cident rays  are  divergent,  where  will  be  the  focus?  If  the  incident 
rays  are  convergent,  where  will  be  the  focus  1 


Fig.  154. 


MIRRORS. 


189 


a 


previous    convergency,     they    are  Fig.  155. 

brought  together  at  a  less  distance 
than  the  principal  focus,  and  meet 
at  o. 

The  images  of  objects  reflected 
by  a  convex  mirror,  we  have  seen, 
are  smaller  than  the  objects  them- 
selves. But  the  concave  mirror, 
when  the  object  is  nearer  to  it  than 
the  principal  focus,  presents  the 
image  larger  than  the  object,  erect, 
and  behind  the  mirror. 

To  explain  this,  let  us  suppose  the  object  a,  fig.  156,  to 
be  placed  before  the  mirror,  and  nearer  to  it  than  the  prin- 
cipal focus.  Then  the  Fig.  156. 
rays  proceeding  from 
the  extremities  of  the 
object  without  inter- 
ruption, would  con- 
tinue to  diverge  in  the 
lines  o  and  n,  as  seen 
behind  the  mirror;  but, 
by  reflection,  they  are 
made  to  diverge  less 
than  before,  and  con- 
sequently to  make  the 
angle  under  which 
they  meet  more  obtuse  ^" 
at  the  eye  b,  than  it 
would  be  if  they  continued  onward  to  e,  where  they  would 
have  met  without  reflection.  The  result,  therefore,  is  to 
render  the  image  h,  upon  the  eye,  as  much  larger  than  the 
object  a,  as  the  angle  at  the  eye  is  more  obtuse  than  the  an- 
gle at  e. 

677.  On  the  contrary,  if  the  object  is  placed  more  remote 
from  the  mirror  than  the  principal  focus,  and  between  the 
focus  and  the  centre  of  the  sphere  of  which  the  reflector  is 
a  part,  then  the  image  will  appear  inverted  on  the  contrary 
side  of  the  centre,  and  farther  from  the  mirror  than  the  ob- 
ject ;  thus,  if  a  lamp  be  placed  obliquely  before  a  concave 

When  will  the  image  from  a  concave  mirror  be  larger  than  the  ob- 
ject, erect,  and  behind  the  mirror  1  Explain  fig.  156,  and  show  why 
the  image  is  larger  than  the  object.  When  will  the  image  from  tht 
concave  mirror  be  inverted,  and  before  the  mirror  1 


I9C  MIRRORS. 

mirror,     as    in  Fig.  157. 

rig.  157,  its  im- 
age will  be  seen 
inverted  in  the 
air,  on  the  con- 
trary side  of 
a  perpendicular 
line  through  the 
centre  of  the 
mirror. 

678.'  From  the  property  of  the  concave  mirror  to  form 
an  inverted  image  of  the  object  suspended  in  the  air,  many 
curious  and  surprising  deceptions  may  be  produced.  Thus, 
when  the  mirror,  the  object,  and  the  light,  are  placed  so 
that  they  cannot  he  seen,  (which  may  he  done  by  placing  a 
screen  before  the  light,  and  permitting  the  reflected  rays  to 
pass  through  a  small  aperture  in  another  screen,)  the  person 
mistakes  the  image  of  the  object  for  its  reality,  and  not  un- 
derstanding the  deception,  thinks  he  sees  persons  walking 
with  their  heads  downwards,  and  cups  of  water  turned  hot 
torn  upwards,  without  spilling  a  drop.  Again,  he  sees  clus- 
ters of  delicious  fruit,  and  when  invited  to  help  himself,  on 
reaching  out  his  hand  for  that  purpose,  he  finds  that  the  ob- 
ject either  suddenly  vanishes  from  his  sight,  owing  to  his 
having  moved  his  eye  out  of  the  proper  range,  or  that  it  is 
intangible. 

This  kind  of  deception  may  be  illustrated  by  any  one 
who  has  a  concave  mirror  only  of  three  or  four  inches  in 
diameter,  in  the  following  manner: 

Suppose  the  tumbler  a,  to  be  filled  with  water,  and  placed 
beyond  the  principal  focus  of  the  concave  mirror,  fig.  158, 
and  so  managed  as  to  be  hid  from  the  eye  c,  by  the  screen 
b.  The  lamp  by  which  the  tumbler  is  illuminated  must  also 
be  placed  behind  the  screen,  and  near  the  tumbler.  To  a 
person  placed  at  c,  the  tumbler  with  its  contents  will  appear 
inverted  at  e,  and  suspended  in  the  air.  By  carefully  mov- 
ing forward,  and  still  keeping  the  eye  in  the  same  line  with 
respect  to  the  mirror,  the  person  may  pass  his  hand  through 
the  shadow  of  the  tumbler ;  but  without  such  conviction,  any 
one  unacquainted  with  such  things,  could  hardly  be  made  to 
believe  that  the  image  was  not  a  reality. 

What  property  has  the  concave  mirror,  by  which  singular  decep- 
tions may  be  produced  7  What  are  these  deceptions  1  Describe  the 
manner  in  which  a  tumbler  with  its  contents  may  be  made  to  seem  in- 
verted in  the  air. 


MIRRORS. 
Fig.  158. 


By  placing  another  screen  between  the  mirror  and  the 
image,  and  permitting  the  converging  rays  to  pass  through 
an  aperture  in  it,  the  mirror  maybe  nearly  covered  from  the 
eye,  and  thus  the  deception  would  be  increased. 

679.  The  image  reflected  frorn  a  concave  mirror,  moves 
in  the  same  direction   with  the  object,  when  the  object  is 
within  the  principal  focus ;  but  when  the  object  is  more  re- 
mote than  the  principal  focus,  the  image  moves  in  a  contra- 
ry direction  from  the  object,  because  the  rays  then  cross 
each  other.     If  a  man  place  himself  directly  before  a  large 
concave  mirror,  but  farther  from  it  than  the  centre  of  con- 
cavity, he  will  see  an  inverted  image  of  himself  in  the  air, 
between  him  and  the  mirror,  but  less  than  himself.     And  if 
he  hold  out  his  hand  towards  the  mirror,  the  hand  of  his 
image  will  come 'out  toward  his  hand,  and  he  may  imagine 
that  he  can  shake  hands  with  his  image.     But  if  he   reach 
his  hand  further  towards  the  mirror,  the  hand  of  the  image 
will  pass  by  his  hand,  and  come  between  his  hand  and  his 
body ;  and  if  he  move  his  hand  toward  either  side,  the  hand 
of  the  image  will  move  in  a  contrary  direction,  so  that  if  the 
object  moves  one  way,  the  image  will  move  the  other. 

680.  The  convave  mirror  having  the  property  of  con- 
verging the  rays  of  light,  is  equally  efficient  in  concentra- 
ting the  rays  of  heat,  either  separately,   or  with  the  light. 
When,  therefore,  such  a  mirror  is  presented  to  the  rays  of 
the  sun,  it  brings  them  to  a  focus,  so  as  to  produce  degrees 
of  heat  in  proportion  to  the  extent  and  perfection  of  its  re- 
flecting surface.     A  metallic  mirror  of  this  kind,  of  only 

Why  does  the  image  move  in  a  contrary  direction  from  its  object, 
when  the  object  is  beyond  the  principal  focus'?  Will  the  concave 
mirror  concentrate  the  rays  of  heat,  as  well  as  those  of  light  7 


i'J2 


MIRRORS. 


four  or  six  inches  in  diameter,  will  fuse  metals,  set  wood  on 
fire,  &c. 

681.  As  the  parallel  rays  of  heat  or  light  are  brought  to 
a  focus  at  the  distance  of  one  quarter  of  the  diameter  of  the 
sphere,  of  which  the  reflector  is  a  section,  so  if  a  luminous 
cr  heated  body  be  placed  at  this  point,  the  rays  from  such 
body  passing  to  the  mirror  will  be  reflected  from  all  parts 
of  its  surface,  in  parallel  lines  ;  and  the  rays  so  reflected, 
by  the  same  law,  will  be  brought  to  a  focus  by  another  mir- 
ror standing  opposite  to  this. 

Fig.  159. 


Suppose  a  red  hot  ball  to  be  placed  in  the  principal  focus 
of  the  mirror  a,  fig.  159,  the  rays  of  heat  and  light  proceed- 
ing from  it  will  be  reflected  in  the  parallel  lines  1,2,  3, 
&c.  The  reason  of  this  is  the  same  as  that  which  causes 
parallel  rays,  when  falling  on  the  mirror,  to  be  converged 
to  a  focus.  The  angles  of  incidence  being  equal  to  those 
of  reflection,  it  makes  no  difference  in  this  respect,  whether 
the  rays  pass  to  or  from  the  focus.  In  one  case,  parallel 
incident  rays  from  the  sun,  are  concentrated  by  reflection ; 
and  in  the  other,  incident  diverging  rays,  from  the  heated 
ball,  are  made  parallel  by  reflection. 

The  rays  therefore,  flowing  from  the  hot  ball  to  the  mir- 
ror a,  are  thrown  into  parallel  lines  by  reflection,  and  these 
reflected  rays,  in  respect  to  the  mirror  b,  become  the  rays 
of  incidence,  which  are  again  brought  to  a  focus  by  reflec- 
tion. 

Suppose  a  luminous  body  be  placed  in  the  focus  of  a  concave  mir- 
ror, in  what  direction  will  its  rays  be  reflected  7  Explain  fig.  159,  and 
show  why  the  rays  from  the  focus  of  a  are  concentrated  in  the  fo- 
cus b. 


LENSES.  193 

Thus  the  heat  of  the  ball,  by  being  placed  in  the  focus  of 
one  mirror,  is  brought  to  a  focus  by  the  reflection  of  the 
other  mirror. 

Several  striking  experiments  may  be  made  with  a  pair 
of  concave  mirrors  placed  facing  each  other,  as  in  the  figure. 
If  a  red  hot  ball  be  placed  in  the  focus  of  a,  and  some  gun- 
powder in  the  focus  of  b,  the  mirrors  being  ten  or  twenty 
feet  apart,  according  to  their  dimensions,  the  powder  will 
flash  "by  the  heat  of  the  ball,  concentrated  by  the  second 
mirror.  To  show  that  it  is  not  the  direct  heat  of  the  ball 
which  sets  fire  to  the  powder,  a  paper  screen  may  be  placed 
between  the  mirrors  until  evexy  thing  is  ready.  The  oper- 
ator will  then  only  have  to  remove  the  screen,  in  order  to 
flash  the  powder. 

To  show  that  heat  and  light  are  separate  principles,  place 
a  piece  of  phosphorus  in  the  focus  of  b,  and  when  the  ball 
is  so  cool  as  not  to  be  luminous,  remove  the  screen,  and  the 
phosphorus  will  instantly  inflame. 

REFRACTION  BY  LENSES. 

.682.  A  Lens  is  a  transparent  body,  generally  made  of 
glass,  and  so  shaped  that  the  rays  of  light  in  passing  through 
it  are  either  collected  together  or  dispersed.  Lens  is  a 
Latin  word,  which  comes  from  lentile,  a  small  flat  bean. 

It  has  already  been  shown,  that  when  the  rays  of  light 
pass  from  a  rarer  to  a  denser  medium,  they  are  refracted,  or 
bent  out  of  their  former  course,  except  when  they  happen 
to  fall  perpendicularly  on  the  surface  of  the  medium. 

The  point  where  no  refraction  is  produced  on  perpendi- 
cular rays,  is  called  the  axis  of  the  lens,  which  is  a  right 
line  passing  through  its  centre,  and  perpendicular  to  both 
its  surfaces. 

In  every  beam  of  light,  the  middle  ray  is  called  its  axis. 

Rays  of  light  are  said  to  fall  directly  upon  a  lens,  when 
their  axes  coincide  with  the  axes  of  the  lens;  otherwise  they 
are  said  to  fall  obliquely. 

The  point  at  which  the  rays  of  the  sun  are  collected,  by 
passing  through  a  lens,  is  called  the  principal  focus  of  that 
lens. 

What  curious  experiments  may  be  made  by  two  concave  mirrors 
aced  opposite  to  each  other  '?  How  may  it  be  shown  that  heat  and 
ight  are  distinct  principles-"?  What  is  a  lens?  What  is  the  axis  of 
a  lens  1  In  what  part  of  a  lens  is  no  refraction  produced  1  Where  is 
the  axis  of  a  Ivam  of  lisfht  1  When  are  rays  of  light  said  to  fall  di- 
rectly upon  a  hns? 


F1 
HI 


194 


LENSES. 


683.  Lenses  are  of  various  kinds,  and  have  received  cer- 
tain names,  depending  on  their  shapes.  The  different  kinds 
are  shown  at  fig.  160. 

Fig.  160. 

b          c  &     e      f     9     fo        i 

\ 


A  prism,  seen  at  a,  has  two  plane  surfaces,  a  r,  and  a  s, 
inclined  to  each  other. 

A  plane  glass,  shown  at  b,  has  two  plane  surfaces,  paral- 
lel to  each  other. 

A  spherical  lens,  c,  is  a  ball  of  glass,  and  has  every  part 
of  its  surface  at  an  equal  distance  from  the  centre. 

A  double  concave  lens,  d,  is  bounded  by  two  convex  sur- 
faces, opposite  to  each  other. 

A  plano-concave  lens,  e,  is  bounded  by  a  convex  surface 
on  one  side,  and  a  plane  on  the  other. 

A  double-concave  lens,  /,  is  bounded  by  two  concave  spher- 
ical surfaces,  opposite  to  each  other. 

A  plano-concave  lens,  g,  is  bounded  by  a  plane  surface 
on  one  side,  and  a  concave  one  on  the  other. 

A  meniscus,  h,  is  bounded  by  one  concave  and  one  convex 
spherical  surface,  which  two  surfaces  meet  at  the  edge  of 
the  lens. 

A  concavo-convex  lens,  i,  is  bounded  by  a  concave  and 
convex  surface,  but  which  diverge  from  each  other,  if  con- 
tinued. 

The  effects  of  the  prism  on  the  rays  of  light  will  be  shown 
in  another  place.  The  refraction  of  the  plane  glass,  bends 
the  parallel  rays  of  lig-ht  equally  towards  the  perpendicular, 
as  already  shown.  The  sphere  is  not  often  employed  as  o 
lens,  since  it  is  inconvenient  in  use. 

684.  CONVEX  LENS.  It  has  been  shown  m  a  former  part 
of  this  article,  that  when  a  ray  of  light  passes  obliquely  out 
of  a  rarer  into  a  denser  medium,  it  is  refracted,  or  turned 
out  of  its  former  course. 

Suppose,  then,  there  is  presented  to  the  rays  of  light,  a 


How  many  kinds  of  lenses  are  mentioned  1     What  is  the  name  of 
each'?     How  arc  each  of  these  lenses  bounded? 


LENSES.  195 

piece  of  glass,  with  its  surface  so  shaped,  that  ail  the  rays, 
except  those  which  pass  through  its  axis,  are  refracted  to- 
wards the  perpendicular,  it  is  obvious  that  they  would  all 
finally  meet  the  perpendicular  ray,  and  there  form  a  focus. 

685.  The  focal  distances  of  convex  lenses,  depend  on  their 
degrees  of  convexity.     The  focal  distance  of  a  single,  or 
oiano-convex  lens,  is  the  diameter  of  a  sphere,  of  which  it 
>s  a  section. 

If  the    whole   circle,  Fig.  161. 

iig.  161,  be  considered 
*he  circumference  of  a 
•sphere,  of  which  the  pla- 
no-convex lens,  b  a,  is  a 
section,  then  the  focus  of 
parallel  rays,  or  the  pr 
cipal  focus,  will  be  at  the 
opposite  side  of  the 
sphere,  or  at  c. 

686.  The   focal    dis- 
tance of  a  double  convex  lens,  is  the  radius,  or  half  the  diam- 
eter of  the  sphere  of  which  it  is  a  part.     Hence  the  plano- 
convex lens,  being  one  half  of  the  double  convex  lens,  the 
latter  has  about  twice  the  refractive  power  of  the  former ; 
for  the  rays  suffer  the  same  degree  of  refraction  in  passing 
out  of  the  one  convex  surface,  that  they  do  in  passing  into 
the  other. 

The  shape  of  the  dou-  Fig.  162. 

ble  convex  lens,  d  c,  fig. 
162,  is  that  of  two  plano- 
convex    lenses,    placed 
with  their  plane  surfaces  / 
in   contact,   and    conse-/ 
quently  the  focal  distance! 
of  this  lens  is  nearly  the\ 
centre  of  the  sphere  of  ' 
which  one  of  its  surfaces 
is   a   part.     If  parallel 
rays  fall   on   a   convex 
lens,  it  is  evident  that  the  ray  only,  which  penetrates  the 
axis  and  passes  towards  the  centre  of  the  sphere,  will  pro- 

On  what  do  the  focal  distances  of  convex  lenses  depend  7  What  is 
the  focal  distance  of  any  plano-convex  lens"?  What  is  the  focal  dis- 
tance of  the  double  convex  lens  7  What  is  the  shape  of  the  double 
convex  lens  7 


196 


LENSES 


ceed  without  refraction,  as  shown  in  the  above  figures.  All 
the  others  will  be  refracted  so  as  to  meet  the  perpendicular 
ray  at  a  greater  or  less  distance,  depending  on  the  convexity 
of  the  lens. 

687.  If  diverging  rays  fall  on  the  surface  of  the  same 
lens,  they  will,  by  refraction,  be  rendered  less  divergent, 
parallel  or  convergent,  according  to  the  degrees  of  their 
divergency,  and  the  convexity  of  the  surface  of  the  lens. 

Thus,  the  diverg-  Fig.  163. 

ing  rays  1,  2,  &c. 
fig.  163,  are  re- 
fracted by  the  lens 
a  o,  in  a  degree  just 
sufficient  to  render 
them  parallel,  and 
therefore  would 
pass  off  in  right 
lines,  indefinitely, 
or  without  ever 
forming  a  focus. 

688.  It  is  obvious  by  tne  same  law,  that  were  the  rays 
less  divergent,  or  were  the  surface  of  the  lens  more  convex, 
the  rays  in  fig.  163  would  become  convergent,  instead  of 
parallel,  because  the  same  refractive  power  which  would 
render  divergent  rays  parallel,  would  make  parallel  rays 
convergent,  and  converging  rays  still  more  convergent. 

Thus  the  pencils  of  converging  rays,  Fig.  164. 

fig.  164,  are  rendered  still  more  conver- 
gent by  their  passage  through  the  lens, 
and  are  therefore  brought  to  a  focus 
nearer  the  lens,  in  proportion  to  their 
previous  convergency. 

689.  The  eye  glasses  of  spectacles 
for  old  people  are  double  convex  lenses, 
more  or  less  spherical,  according  to  the 
age  of  the  person,  or  the  magnifying 
power  required. 

The  common  burning  glasses,  which  are  used  for  light- 
ing cigars,  and  sometimes  for  kindling  fires,  are  also  convex 
lenses.  Their  effect  is  to  concentrate  to  a  focus,  or  point, 
the  heat  of  the  sun  which  falls  on  their  whole  surface;  and 

How  are  divergent  rays  affected  by  passing  through  a  convex  lens  1 
What  is  its  effect  on  parallel  rays  1  What  is  its  effect  on  converging 
rays  ?  What  kind  of  lenses  are  spectacle  glasses  for  old  people  1 


LENSES,  197 

hence  the  intensity  01"  their  effects  is  in  proportion  to  the 
extent  of  their  surfaces,  and  their  focal  lengths. 

One  of  the  largest  burning  glasses  ever  constructed,  was 
made  by  Mr.  Parker,  of  London.  It  was  three  feet  in  diam- 
eter, with  a  focal  distance  of  three  feet  nine  inches.  But 
in  order  to  increase  its  power  still  more,  he  employed  ano- 
ther lens  about  a  foot  in  diameter,  to  bring  its  rays  to  a 
smaller  focal  point.  This  apparatus  gave  a  most  intense 
degree  of  heat,  when  the  sun  was  clear,  so  that  20  grains 
of  gold  were  melted  by  it  in  4  seconds,  and  ten  grains  of 
platina,  the  most  infusible  of  all  metals,  in  3  seconds. 

690.  It  has  been  explained,  that  the  reason  why  the  con- 
vex mirror  diminishes  the  images  of  objects  is,  that  the  rays 
which  come  to  the  eye  from  the  extreme  parts  of  the  object 
are  rendered  less  convergent  by  reflection,  from  the  convex 
surface,  and  that,  in  consequence,  the  angle  of  vision  is  made 
more  acute. 

Now,  the  refractive  power  of  the  convex  lens  has  exactly 
the  contrary  effect,  since  by  converging  the  rays  flowing 
from  the  extremities  of  an  object,  the  visual  angle  is  rendered 
more  obtuse,  and  therefore  all  objects  seen  through  it  appeal- 
magnified. 

Suppose  the  object  a,  fig. 
165,  appears  to  the  naked 
eye  of  the  length  represented 
in  the  drawing.  Now,  as 
the  rays  coming  from  each 
end  of  the  object,  form,  by 
their  convergence  at  the  eye,  the  visual  angle,  or  the  angle 
under  which  the  object  is  seen,  and  we  call  objects  large  or 
small,  in  proportion  as  this  angle  is  obtuse  or  acute,  if  there- 
fore the  object  a  be  withdrawn  further  from  the  eye,  it  is 
apparent  that  the  rays  o,  0,  proceeding  from  its  extremities, 
will  enter  the  eye  under  a  more  acute  angle,  and  therefore, 
that  the  object  will  appear  diminished  in  proportion.  This 
is  the  reason  why  things  at  a  distanc.e  appear  smaller  than 
when  near  us.  When  near,  the  visual  angle  is  increased, 
and  when  at  a  distance,  it  is  diminished. 


What  is  said  to  be  the  diameter  of  Mr.  Parker's  great  convex  lens  7 
What  is  the  focal  distance  of  this  Jens'?  What  is  said  of  its  heating 
power!  What  is  the  visual  angle!  Why  does  the  same  object, 
wnen  at  a  distance,  appear  smaller  than  when  near! 

17* 


198 


LENSES. 


691.  The  effect  of  the  convex  lens  is  Fig.  166. 
to  increase  the  visual  angle,  by  bending 

the  rays  of  light  coming  from  the  object, 
so  as  to  make  them  meet  at  the  eye  more 
obtusely;  and  hence  it  has  the  same  ef- 
fect, in  respect  to  the  visual  angle,  as 
bringing  the  object  nearer  the  eye.  This 
is  shown  by  fig.  166,  where  it  is  obvious, 
that  did  the  rays  flowing  from  the  extrem- 
ities of  the  arrow  meet  the  eye  without 
refraction,  the  visual  angle  would  be  less,  and  therefore  the 
object  would  appear  shorter.  Another  effect  of  the  convex 
lens,  is  to  enable  us  to  see  objects  nearer  the  eye,  than  with- 
out it,  as  will  be  explained  under  the  article  vision. 

Now,  as  the  rays  of  light  flow  from  all  parts  of  a  visible 
object  of  whatever  shape,  so  the  breadth,  as  well  as  the 
length,  is  increased  by  the  convex  lens,  and  thus  the  whole 
object  appears  magnified. 

692.  CONCAVE  LENS. — The  effect  of  the  concave  lens  is 
directly  opposite  to  that  of  the  convex.     In  other  terms,  by 
a  concave  lens,  parallel  rays  are  rendered  diverging,  con- 
verging rays  have  their  convergency  diminished,  and  di- 
verging rays  have  their  divergency  increased,  according  to 
the  concavity  of  the  lens. 

These  glasses,  therefore,  exhibit  things  smaller  than  they 
really  are,  for  by  diminishing  the  convergence  of  the  rays 
coming  from  the  extreme  points  of  an  object,  the  visual  an- 
gle is  rendered  more  acute,  and  hence  the  object  appears 
diminished  by  this  lens,  for  the  opposite  reason  that  it  is 
increased  by  the  convex  lens.  This  will  be  made  plain  by 
the  two  following  diagrams. 

Suppose  the  object  a  b,  fig.  Fig- *6~' 

167,  to  be  placed  at  such  a  dis- 
tance from  the  eye,  as  to  give 
the  rays  flowing  from  it,  the 
degrees  of  convergence  repre- 
sented in  the  figure,  and  sup- 
pose that  the  rays  enter  the  eye 
under  such  an  angle  as  to  make 
the  object  appear  two  feet  in 
lenp-th. 


What  is  the  effect  of  the  convex  lens  on  the  visual  angle?  "Why 
does  an  object  appear  larger  through  the  convex  lens  than  otherwise  ? 
What  is  the  effect  of  the  concave  lens  1  What  effect  does  this  lens  have 
upon  parallel,  diverging,  and  converging  rays  ?  Why  do  objects  ap- 
pear smaller  through  this  glass  than  they  do  to  the  naked  eye  ? 


199 


Now,  the  length  of  the  same  Fig.  168. 

object,  seen  through  the  concave 
lens,  fig.  168»  will  appear  dimin- 
ished, because  the  rays  coming 
from  it  are  bent  outwards,  or 
made  less  convergent  by  refrac- 
tion, as  foen  in  the  figure,  and 
conseqrmtly  the  visual  angle  is 
more  riute  than  when  the  same  object  is  seen  by  the  naked 
eye.  Its  length,  therefore,  will  appear  less,  in  proportion 
as  the  rays  are  rendered  less  convergent. 

The  spectacle  glasses  of  short-sighted  people  are  concave 
leases,  by  which  the  images  of  objects  are  formed  further 
J  ack  in  the  eye  than  otherwise,  as  will  be  explained  under 
he  next  article. 

VISION. 

693.  In  the  application  of  the  principles  of  optics  to  the 
explanation  of  natural  phenomena,  it  is  necessary  to  give  a 
lescription  of  the  most  perfect  of  all  optical  instruments, 
he  eye. 

694.  Fig.   169   is  a  Fig.  169. 
vertical   section  of  the 

numan  eye.  Its  form 
is  nearly  globular,  with 
a  slight  projection  or 
elongation  in  front.  It 
consists  of  four  coats, 
or  membranes;  name- 
ly, the  sclerotic,  the 
cornea,  the  cAoroid,  and 
the  retina.  It  has  two 
fluids  confined  within 
these  membranes,  called  the  aqueous,  and  the  vitreous  hum- 
ours, and  one  lens,  called  the  crystalline.  The  sclerotic 
coat  is  the  outer  and  strongest  membrane,  and  its  anterior 
part  is  well  known  as  the  white  of  the  eye.  This  coat  is 
marked  in  the  figure  a,  a,  a,  a.  It  is  joined  to  the  cornea, 

Explain  figures  1C7  and  168,  and  show  the  reason  why  the  same  ob- 
ject appears  smaller  through  168.  What  defect  in  the  eye  requires  con- 
cave lenses  1  What  is  the  most  perfect  of  all  optical  instruments'? 
What  is  the  form  of  the  human  eye  1  How  many  coats,  or  membranes, 
lias  the  eye!  What  are  they  called.'?  How  many  fluids  has  the  eye, 
and  what  are  they  called "?  What  is  the  lens  of  the  eye  called  7  What 
coat  forms  the  white  of  the  eye  1 


200  VISION. 

b,  bt  which  is  tne  transparent  membrane  in  front  of  the  eye, 
through  which  we  see.  The  choroid  coat  is  a  thin,  deli- 
cate membrane,  which  lines  the  sclerotic  coat  on  the  inside. 
On  the  inside  of  this  lies  the  retina,  d,  d,  d,  d,  which  is  the 
innermost  coat  of  all,  and  is  an  expansion,  or  continuation, 
of  the  optic  nerve  o.  This  expansion  of  the  optic  nerve  is 
the  immediate  seat  of  vision.  The  iris,  0,  0,  is  seen  through 
the  cornea,  and  is  a  thin  membrane,  or  curtain,  of  different 
colours  in  different  persons,  and  therefore  gives  colour  to 
the  eyes.  In  black  eyed  persons  it  is  black,  in  blue  eyed 
persons  it  is  blue,  &c.  Through  the  iris,  is  a  circular  open- 
ing, called  the  pupil,  which  expands  or  enlarges  when  the 
light  is  faint,  and  contracts  when  it  is  too  strong.  The  space 
between  the  iris  and  the  cornea  is  called  the  anterior  chamber 
of  the  eye,  and  is  filled  with  the  aqueous  humour,  so  called 
from  its  resemblance  to  water.  Behind  the  pupil  and  iris 
is  situated  the  crystalline  lens  t,  which  is  a  firm  and  per- 
fectly transparent  body,  through  which  the  rays  of  light 
pass  from  the  pupil  to  the  retina.  Behind  the  lens  is  situa- 
ted the  posterior  chamber  of  the  eye,  which  is  filled  with 
the  vitreous  humour,  v,  v.  This  humour  occupies  much 
the  largest  portion  of  the  whole  eye,  and  on  it  depends  the 
shape  and  permanency  of  the  organ. 

695.  From  the  above  description  of  the  eye,  it  will  be 
easy  to  trace  the  progress  of  the  rays  of  light  through  its 
several  parts,  and  to  explain  in  what  manner  vision  is  per- 
formed. 

In  doing  this,  we  must  keep  in  mind  that  the  rays  of  light 
proceed  from  every  part  and  point  of  a  visible  object,  as 
heretofore  stated,  and  that  it  is  necessary  only  for  a  few  of 
the  rays,  when  compared  with  the  whole  number,  to  enter 
the  eye,  in  order  to  make  the  object  visible. 

Thus,  the  object  a  b.  fig.  170,  being  placed  in  the 
light,  sends  forth  pencils  of  rays  in  all  possible  direc- 


Describe  where  the  several  coats  and  humours  are  situated.  "What 
«s  the  iris  1  What  is  the  retina  1  Where  is  the  sense  of  vision  ?  What 
«s  the  design  of  fig.  170 1  What  is  said  concerning  the  small  number 
of  the  rays  which  enter  the  eye  from  a  visible  object  1  Explain  the  de«. 
sign  of  fig.  170. 


VISION. 


which  will 
in  any  posi- 


dons,  some  of 
strike  the  eye 
tion  where  it  is  visible. 
These  pencils  of  rays  not 
only  flow  from  the  points 
designated  in  the  figure,  but 
in  the  same  manner  from 
every  other  point  on  the  sur- 
face of  a  visible  object.  To 
render  an  object  visible, 
therefore,  it  is  only  neces- 
sary that  the  eye  should  col- 
lect and  concentrate  a  suffi- 
cient number  of  these  rays  on 
the  retina,  to  form  its  image 
there,  and  from  this  image  § 
the  sensation  of  vision  is  ex- 
cited. 

696.  From  the  luminous  body  Z,  fig.  171,  the  pencils  of 
ravs  flow  in  all  directions,  but  it  is  only  by  those  which  en- 
Fig.  171. 


ter  the  pupil,  that  we  gain  any  knowledge  of  its  existence ; 
and  even  these  would  convey  to  the  mind  no  distinct 
idea  of  the  object,  unless  they  were  refracted  by  the  hu- 
mours of  the  eye,  for  did  these  rays  proceed  in  their  natural 
state  of  divergence  to  the  retina,  the  image  there  formed 
would  be  too  extensive,  and  consequently  too  feeble  to  give 
a  distinct  sensation  of  the  object. 

It  is,  therefore,  by  the  refracting  power  of  the  aqueous 
humour,  and  of  the  crystalline  lens,  that  the  pencils  of  rays 
are  so  concentrated  as  to  form  a  perfect  picture  of  the  object 
on  the  retina. 

We  have  already  seen,  that  when  the  rays  of  light  are 
made  to  cross  each  other  by  reflection  from  the  concave  mir- 


Why  would  not  the  rays  of  light  give  a  distinct  idea  of  the  object, 
without  refraction  by  the  humovus  of  the  eye  7 


202  VISION. 

ror,  the  image  of  the  object  is  inverted  ;  the  same  happens 
when  the  rays  are  made  to  cross  each  other  by  refraction 
through  a  convex  lens.  *  This,  indeed,  must  be  a  necessary 
consequence  of  the  intersection  of  the  rays:  for,  as  light 
proceeds  in  straight  lines,  those  rays  which  come  from  the 
lower  part  of  an  object,  on  crossing  those  which  come  from 
its  upper  part,  will  represent  this  part  of  the  picture  on  the 
upper  half  of  the  retina,  and,  for  the  same  reason,  the  upper 
part  of  the  object  will  be  painted  on  the  lower  part  of  the 
retina. 

697.  Now,  all  objects  are  represented  on  the  retina  in  an 
inverted  position ;  that  is,  what  we  call  the  upper  end  of  a 
vertical  object,  is  the  lower  end  of  its  picture  on  the  retina, 
and  so  the  contrary. 

This  is  readily  pioved  by  taking  the  eye  of  an  ox,  ana 
cutting  away  the  sclerotic  coat,  so  as  to  make  it  transparent 
on  the  back  part,  next  the  vitreous  humour.  If  now  a  piece 
of  white  paper  be  placed  on  this  part  of  the  eye,  the  images 
of  objects  will  appear  figured  on  the  paper  in  an  inverted 
position.  The  same  effect  will  be  produced  on  looking  at 
things  through  an  eye  thus  prepared;  they  will  appear  in- 
verted. 

The  actual  position  of  the  vertical  object  a,  fig.  172,  39 
painted  on  the  retina,  is  therefore  such  as  is  represented  by 
the      figure. 
The        rays 
from  its    up- 
per   extremi- 
ty,      coming 
in    divergent 
lines,  are  con- 
verged by  the  o ] 
crystalline 
lens,  and  fall 

on  the  retina  at  o ;  while  those  from  its  lower  extremity,  by 
the  same  law,  fall  on  the  retina  at  c. 

698.  In  order  that  vision  may  be  perfect,  it  is  necessary 
that  the  images  of  objects  should  be  formed  precisely  on 
the  retina,  and  consequently,  if  the  refractive  power  of  the 
eye  be  too  small,  or  too  great,  the  image  will  not  fall  ex 


Explain  how  it  is  that  the  images  of  objects  are  inverted 
ina.      What  experiment  proves  that  the  images  of  objects  a 


on  the  ret- 
are  inverted 

on  the  retina  1   'Explain  fig.  172.     Suppose  the  refractive  power  of  the 
eye  is  too  great,  or  too  little,  why  will  vision  be  imperfect  ? 


VISION.  203 

actly  on  the  seat  of  vision,  but  will  be  formed  either  before, 
or  tend  to  form  behind  it.  In  both  cases,  perhaps,  an  out- 
line of  the  object  may  be  visible,  but  it  will  be  confused  and 
indistinct. 

699.  If  the  cornea  is  too  convex,  or  prominent,  the  imag*e 
will  be  formed  before  it  reaches  the  retina,  for  the  same  rea- 
son, that  of  two  lenses,  that  which  is  most  convex  will  have 
the  least  focal  distance.  Such  is  the  defect  in  the  eyes  of 
persons  who  are  short  sighted,  and  hence  the  necessity  of 
their  bringing  objects  as  near  the  eye  as  possible,  so  as  to 
make  the  rays  converge  at  the  greatest  distance  behind  the 
crystalline  lens. 

The  effect  of  uncommon  convexity  in  the  cornea  on  the 
rays  of  light,  is  shown  at  fig.  173,  where  it  will  be  ob- 


Fig.  173. 


served  that  the  image,  instead  of  being  formed  on  the  retina 
r,  is  suspended  in  the  vitreous  humour,  in  consequence  of 
there  being  too  great  a  refractive  power  in  the  eye.  It  is 
hardly  necessary  to  say,  that  in  this  case,  vision  must  be 
very  imperfectly  performed. 

This  defect  of  sight  is  remedied  by  spectacles,  the  glasses 
of  which  are  concave  lenses.  Such  glasses,  by  rendering 
the  rays  of  light  less  convergent,  before  they  reach  the  eye, 
counteract  the  too  great  convergent  power  of  the  cornea  and 
lens,  and  thus  throw  the  image  on  the  retina. 

70Q.  If,  on  the  contrarv,  the  humours  of  the  eye,  in  con- 
sequence of  age,  or  c«uv  other  cause,  have  become  less  in 
quantity  than  ordinary,  tne  eyeball  will  not  be  sufficiently 
distended,  and  the  cornea  will  become  too  flat,  or  not  suffi- 
ciently convex,  to  make  the  rays  of  light  meet  at  the  proper 
place,  and  the  image  will  therefore  tend  to  be  formed  be- 


If  the  cornea  is  too  convex,  where  will  the  image  be  formed  1  How 
is  the  sight  improved,  when  the  cornea  is  too  convex  1  How  do  such 
lenses  act  to  improve  the  sight  1  Where  do  the  rays  tend  to  meet  when 
tne  cornea  is  not  sufficiently  convex  1 


204  VISION. 

yond  the  retina,  instead  of  before  it,  as  in  the  other  case. 
Hence,  aged  people,  who  labour  under  this  defect  of  vision, 
cannot  see  distinctly  at  ordinary  distances,  but  are  obliged 
to  remove  the  object  as  far  from  the  eye  as  possible,  so  as  to 
make  its  refractive  power  bring  the  image  within  the  seat 
of  vision. 

The  defect  arising  from  this  cause  is  represented  by  fig- 
ure 174,  where  it  will  be  observed  that  the  image  is  formed 
Fis:.  174. 


behind  the  retina,  showing  that  the  convexity  of  the  cornea 
is  not  sufficient  to  bring  the  image  within  the  seat  of  dis- 
tinct vision.  This  imperfection  of  sight  is  common  to  aged 
persons,  and  is  corrected  in  a  greater  or  less  degree  by 
double  convex  lenses,  such  as  the  common  spectacle  glasses. 
Such  glasses,  by  causing  the  rays  of  light  to  converge,  be- 
fore they  meet  the  eye,  assist  the  refractive  power  of  the 
crystalline  lens,  and  thus  bring  the  focus,  or  image,  within 
the  sphere  of  vision. 

701.  It  has  been  considered  difficult  to  account  for  the 
reason  why  we  see  objects  erect,  when  they  are  painted  on 
the  retina  inverted,  and  many  learned  theories  have  been 
written  to  explain-  this  fact.  But  it  is  most  probable  that 
this  is  owing  to  habit,  and  that  the  image,  at  the  bottom  of 
the  eye,  has  no  relation  to  the  terms  above  and  below,  but  to 
the  position  of  our  bodies,  and  other  things  which  surround 
us.  The  term  perpendicular,  and  the  idea  which  it  con- 
veys to  the  mind,  is  merely  relative  ;  but  when  applied  to  an 
object  supported  by  the  earth,  and  extending  towards  the 
skies,  we  call  the  body  erect,  because  it  coincides  with  the 
position  of  our  own  bodies,  and  we  see  it  erect  for  the  same 
reason.  Had  we  been  taught  to  read  by  turning  our  books 
upside  down,  what  we  now  call  the  upper  part  of  the  book 

How  is  vision  assisted  when  the  eye  wants  convexity  1  How 
clo  convex  lenses  help  the  sight  of  aged  people  1  Why  do  we  see  things 
erect,  when  the  images  are  inverted  on  the  retina  1 


VISION. 


205 


would  have  been  its  under  part,  and  that  reading  would  have 
been  as  easy  in  that  position  as  in  any  other,  is  plain  from 
the  fact  that  printers  read  their  types,  when  set  up,  as  rea- 
dily as  they  do  its  impressions  on  paper. 

702.  Angle  of  Vision. — The  angle  under  which  the  rays 
of  light,  coming  from  the  extremities  of  an  object,  cross  each 
other  at  the  eye,  bears  a  proportion  directly  to  the  length, 
and  inversely  to  the  distance  of  the  object. 

Suppose  the  object  a  b,  fig.  175,  to  be  four  feet  long,  and 
-o  be  placed  ten  feet  from  the  eye,  then  the  rays  flowing 
from  its  extremities,  would  intersect  each  other  at  the  eye, 
Fig.  175. 


under  a  given  angle,  which  will  always  be  the  same  when 
the  object  is  at  the  same  distance.  If  the  object  be  gradu- 
ally moved  towards  the  eye,  to  the  place  c  d,  then  the  angle 
will  be  gradually  increased  in  quantity,  and  the  object  will 
appear  larger,  since  its  image  on  the  retina  will  be  increas- 
ed in  length  in  the  proportion  as  the  lines  i  i  are  wider  apart 
than  o  o.  On  the  contrary,  were  a  b  removed  to  a  greater  dis- 
tance from  the  first  position,  it  is  obvious  that  the  angle 
would  be  diminished  in  proportion. 

The  lines  thus  proceeding  from  the  extremities  of  an  ob- 
iect,  and  representing  the  rays  of  light,  form  an  angle  at  the 
eye,  which  is  called  the  visual  angle,  or  the  angle  under 
which  things  are  seen.  These  lines  a  n  b,  therefore, 
brm  one  visual  angle,  and  the  lines  end  another  visual 
mgle. 

We  see  from  this  investigation,  that  the  apparent  magni- 
•ude  of  objects  depending  on  the  angles  of  vision,  will  vary 
tccording  to  their  distances  from  the  eye,  and  that  these 
magnitudes  diminish  in  a  proportion  inversely  as  their  dis- 

What  is  the  visual  angle'?     How  may  the  visual  angle  of  the  same 
object  be  increased  or  diminished  1   When  do  objects  of  different  mag 
litudes  form  the  same  visual  angle  1 
18 


206  VISION. 

tances  increase.  We  learn,  also,  from  the  same  principles, 
that  objects  of  different  magnitudes  may  be  so  placed,  with 
respect  to  the  eye,  as  to  give  the  same  visual  angle,  and 
thus  to  make  their  apparent  magnitudes  equal.  Thus  the 
three  arrows,  a,  e,  and  m,  though  differing  so  much  in 
length,  are  all  seen  under  the  same  visual  angle. 

703.  In  the  apparent  magnitude  of  objects  seen  through  a 
lens,  or  when  their  images  reach  the  eye  by  reflection  from 
a  mirror,  our  senses  are  chiefly,  if  not  entirely,  guided  by 
the  angle  of  vision.     In  forming  our  judgment  of  the  sizes 
of  distant  objects,  whose  magnitudes  were  before  unknown, 
we  are  also  guided  more  or  less  by  the  visual  angle,  though 
in  this  case  we  do  not  depend  entirely  on  the  sense  of  vision. 
Thus,  if  we  see  two  balloons  floating  in  the  air,  one  of  which 
is  larger  than  the  other,  we  judge  of  their  comparative  mag- 
nitudes by  the  difference  in  their  visual  angles,  and  of  their 
real  magnitudes  by  the  same  angles,  and  the  distance  \ve 
suppose  them  to  be  from  us. 

But  when  the  object  is  near  us,  and  seen  with  the  naked 
eye,  we  then  judge  of  the  magnitude  by  our  experience,  and 
not  entirely  by  the  visual  angle.  Thus,  the  three  arrows, 
a,  e,  m,  fig.  175,  all  of  them  make  the  same  angle  on  the 
eye,  and  yet  we  know,  by  further  examination,  that  they  are 
all  of  different  lengths.  And  so  the  two  arrows  a  b,  and  c 
d,  though  seen  under  different  visual  angles,  wrill  appear  of 
the  same  size,  because  experience  has  taught  us  that  this 
difference  depends  only  on  the  comparative  distance  of  the 
two  objects. 

704.  As  the  visual  angle  diminishes  inversely  in  propor- 
tion as  the  distance  of  the  object  increases,  so  when  the  dis- 
tance is  so  great  as  to  make  the  angle  too  minute  to  be  per- 
ceptible to  the  eye,  then  the  object  becomes  invisible.   Thus, 
when  we  watch  an  eagle,  flying  from  us,  theano-le  of  vision 
is  gradually  diminished,  until  the  rays  proceeding  from  the 
bird  form  an  image  on  the  retina  too  small  to  excite  sensa- 
tion, and  then  we  say  the  ea^le  has  flown  out  of  sight. 

The  same  principle  holds  with  respect  to  objects  which 
are  near  the  eye,  but  are  too  small  to  form  an  image  on  the 
retina  which  is  perceptible  to  the  senses.  Such  objects,  to 

Explain  fig.  175.  Under  what  circumstances  is  our  sense  of  vision 
guided  entirely  by  the  visual  angle  *?  How  do  we  judge  of  the  mag- 
nitudes of  distant  objects  ?  How  do  we  judge  of  the  comparative  size 
o*  objects  near  us  1  When  does  a  retreating  object  become  invisible 
to  the  eye  1 


VISION.  207 

ue  naked  eye,  are  of  course  invisible,  but  when  the  Tisual 
a*gle  is  enlarged,  by  means  of  a  convex  lens,  they  become 
visible;  that  is,  their  images  on  the  retina  excite  sensation. 

705.  The  actual  size  of  an  image  on  the  retina,  capable 
of  exciting  sensation,  and  consequently  of  producing  vision, 
may  be  too  small  for  us  to  appreciate  by  any  of  our  other 
senses  ;  for  when  we  consider  how  much  smaller  the  image 
must  be  than  the  object,  and  that  a  human  hair  can  be  dis- 
tinguished by  the  naked  eye  at  the  distance  of  twenty  or 
thirty  feet,  we  must  suppose  that  the  retina  is  endowed  with 
the  most  delicate  sensibility,  to  be  excited  by  a  cause  so  mi- 
nute.    It  has  been  estimated  that  the  image  of  a  man,  on  the 
retina,  seen  at  the  distance  of  a  mile,  is  not  more  than  the 
five  thousandth  part  of  an  inch  in  length. 

706.  On  the  contrary,  if  the  object  be  brought  too  near 
the  eye,  its  image  becomes  confused  and  indistinct,  because 
the  rays  flowing  from  it,  fall  on  the  crystalline  lens  in  a 
state  too  divergent  to  be  refracted  to  a  focus  on  the  retina. 

This  will  be  apparent  Fig.  176. 

by  fig.  176,  where  we 
suppose  that  the  object  a, 
is  brought  within  an  inch 
or  two  of  the  eye,  and  that 
the  rays  proceeding  from 
it  enter  the  pupil  so  ob- 
liquely as  not  to  be  re- 
fracted by  the  lens,  so  as 
to  form  a  distinct  image. 

Could  we  see  objects  distinctly  at  the  shortest  distance, 
we  should  be  able  to  examine  things  that  are  now  invisible, 
since  the  visual  angle  would  then  be  increased,  and  conse- 
quently the  image  on  the  retina  enlarged,  in  proportion  as 
objects  were  brought  near  the  eye. 

This  is  proved  by  intercepting  the  most  divergent  rays ; 
in  which  case  an  object  may  be  brought  near  the  eye,  and 
will  then  appear  greatly  magnified.  Make  a  small  orifice, 
as  a  pin-hole,  through  a  piece  of  dark  coloured  paper,  and 
then  look  through  the  orifice  at  small  objects,  such  as  the 

How  does  a  convex  lens  act  to  make  us  see  objects  which  are  invisi- 
ble without  it  1  What  is  said  of  the  actual  size  of  an  image  on  the  ret- 
ina 1  Why  are  objects  indistinct,  when  brought  too  near  the  eye  ri 
Suppose  objects  could  be  seen  distinctly  within  an  inch  or  two  of  the 
eye,  how  would  their  dimensions  be  affected  1  How  is  it  proved  that 
objects  placed  near  the  eye  are  magnified  1  How  does  a  small  orifice 
enable  us  to  see  an  object  distinctly  near  the  eyel 


208 


MICROSCOPE. 


letters  of  a  printed  book.  The  letters  will  appear  much 
magnified.  The  rays,  in  this  case,  are  refracted  to  a  focus, 
on  the  retina,  because  the  small  orifice  prevents  those  which 
are  most  divergent  from  entering  the  eye,  so  that  notwith- 
standing the  nearness  of  the  object,  the  rays  which  form  the 
image  are  nearly  parallel. 

OPTICAL  INSTRUMENTS. 

707.  Single  Microscope. — The  principle  of  the   single 
microscope,  or  convex  lens,  will  be  readily  understood,  if 
the  pupil  will  remember  what  has  been  said  on  the  refrac- 
tion of  lenses,  in  connexion  with  the  facts  just  stated.     For, 
the  reason  why  objects  appear  magnified  through  a  convex 
lens,  is  not  only  because  the  visual  angle  is  increased,  but 
because  when  brought  near  the  eye,  the  diverging  rays  from 
the  object  are  rendered  parallel  by  the  lens,  and  are  thus 
thrown  into  a  condition  to  be  brought  to  a  focus  in  the  pro- 
per place  by  the  humours. 

Let     a,    fig.  Fig.  177. 

177,  be  the  dis- 
tance at  which 
an  object  can 
be  seen  dis- 
tinctly, and  b, 
the  distance 
at  which  the 
same  object  is  seen  through  the  lens,  and  suppose  th,e  dis- 
tance of  at  from  the  eye,  be  twice  that  of  b.  Then,  because 
the  object  is  at  half  the  distance  that  it  was  before,  it  will 
appear  twice  as  large ;  and  had  it  been  seen  one  third,  one 
fourth,  or  one  tenth  its  former  distance,  it  would  have  been 
magnified  three,  four,  or  ten  times,  and  consequently  its  sur 
face  would  be  increased  9,  16,  or  100  times. 

708.  The  most  powerful  single  microscopes  are  made  of 
minute  globules  of  glass,  which  are  formed  by  melting  the 
ends  of  a  few  threads  of  spun  glass  in  a  candle.     Small 
globules  of  water  placed  in  an  orifice  through  a  piece  of 
tin,  or  other  thin  substance,  will  also  make  very  powerful 
microscopes.     In  these  minute  lenses,  the  focal  distance  is 
only  a  tenth  or  twelfth  part  of  an  inch  from  the  lens,  and 

Why  does  a  convex  lens  make  an  object  distinct  when  near  the  eye"? 
Explain  fig.  177.  How  are  the  most  powerful  single  microscopes 
made? 


MICROSCOPE. 


209 


therefore  the  eye,  as  well  as  the  object  to  be  magnified,  must 
be  brought  very  near  the  instrument. 

709.  The  Compound  Microscope  consists  of  two  convex 
lenses,  by  one  of  which  the  image  is  formed  within  the  tube 
of  the  instrument,  and  by  the  other  this  image  is  magnified, 
as  seen  by  the  eye ;  so  that  by  this  instrument  the  object  it- 
self  is  not  seen,  as  with  the  single  microscope,  but  we  see 
only  its  magnified  image. 

The  small  lens  placed  near  the  object,  and  by  which  its 
image  is  formed  within  the  tube,  is  called  the  object  glass, 
while  the  larger  one,  through  which  the  image  is  seen,  is 
called  the  eye  glass. 

This  arrangement  is  represented  at  fig.  178.     The  object 

a  is  placed  a  little  beyond  the  focus  of  the  object  glass  b,  by 

which  an  inverted  and  enlarged  image  of  it  is  formed  within 

the  instrument  at  c.      This  image  is  seen  through  the  eye 

Fig.  178. 


glass  d,  by  which  it  is  again  magnified,  and  it  is  at  last 
figured  on  the  retina  in  its  original  position. 

These  glasses  are  set  in  a  case  of  brass,  the  object  glass 
being  made  to  take  out,  go  that  others  of  different  magnify- 
ing powers  may  be  used,  as  occasion  requires. 

710.  The  Solar  Microscope  consists  of  two  lenses,  one 
of  which  is  called  the  condenser,  because  it  is  employed  to 
concentrate  the  rays  of  the  sun,  in  order  to  illuminate  more 
strongly  the  object  to  be  magnified.  The  other  is  a  double 
convex  lens,  of  considerable  magnifying  power,  by  which 
the  image  is  formed.  In  addition  to  these  lenses,  there  is  a 
plain  mirror,  or  piece  of  common  looking  glass,  which  can 

How  many  lenses  foitn  the  compound  microscope  1  Which  is  the  ob- 
ject and  which  the  eye  glass  1  Is  the  object  seen  with  this  instrument, 
or  only  its  image  1  Explain  fig.  178,  and  show  where  the  image  is 
formed  in  this  tube.  How  many  lenses  has  the  solar  microscope? 
Why  is  one  of  the  lenses  of  the  solar  microscope  called  the  condenser  1 
Describe  the  uses  of  the  two  lenses  ana  tr:e  reflector. 

18* 


210 


MICROSCOPE. 


be  moved  in  any  direction,  and  which  reflects  the  rays  of  the 
sun  on  the  condenser. 

The  object  a,  fig.  179,  being  placed  nearly  in  the  focus  of 
the  condenser  b,  is   strongly  illuminated,  in   consequence 


of  the  rays  of  the  sun  being  thrown  on  b,  by  the  mirror  c. 
The  object  is  not  placed  exactly  in  the  focus  of  the  conden- 
ser, because,  in  most  cases,  it  would  be  soon  destroyed  by  its 
heat,  and  because  the  focal  point  would  illuminate  only  a 
small  extent  of  surface,  but  may  be  exactly  in  the  focus  of 
the  small  lens  d,  by  which  no  such  accident  can  happen. 
The  lines  o  0,  represent  the  incident  rays  of  the  sun,  which 
are  reflected  on  the  condenser. 

When  the  solar  microscope  is  used,  the  room  is  darkened, 
the  only  light  admitted  being  that  which  is  thrown  on  the 
object  by,  the  condenser,  which  light  passing  through  the 
small  lens,  gives  the  magnified  shadow  e,  of  the  small  object 
fi,  on  the  wall  of  the  room,  or  on  a  screen.  The  tube  con- 
taining the  two  lenses  is  passed  through  the  window  of  the 
room,  the  reflector  remaining  outside. 

In  the  ordinary  use  of  this  instrument,  the  object  itself  is 
not  seen,  but  only  its  shadow  on  the  screen,  and  it  is  not  de- 
signed for  the  examination  of  opaque  objects. 

711.  When  the  small  lens  of  the  solar  microscope  is 
of  great  magnifying  power,  it  presents  some  of  the  most 
striking  and  curious  of  optical  phenomena.  The  shadows 
of  mites  from  cheese,  or  figs,  appear  nearly  two  feet  in 
length,  presenting  an  appearance  exceedingly  formidable 
and  disgusting ;  and  the  insects  from  common  vinegar  ap- 
pear eight  or  ten  feet  long,  and  in  perpetual  motion,  resem- 
bling so  many  huge  serpents. 


Is  the  object,  or  only  the  shadow,  seen  by  this  instrument  ? 


TELESCOPE.  211 

TELESCOPE. 

712.  The  Telescope  is  an  optical  instrument,  employed  to 
view  distant  bodies,  and,  in  effect,  to  bring  them  nearer  the 
eye,  by  increasing  the  apparent  angles  under  which  such 
objects  are  seen. 

These  instruments  are  of  two  kinds,  namely,  refracting 
and  reflecting  telescopes.  In  the  first  kind,  the  image  of  the 
object  is  seen  with  the  eye  directed  towards  it;  in  the  sec-  i 
ond  kind,  the  image  is  seen  by  reflection  from  a  mirror, 
while  the  back  is  towards  the  object,  or  by  a  double  reflec- 
tion, with  the  face  towards  the  object. 

The  telescope  is  the  most  important  of  all  optical  instru- 
ments, since  it  unfolds  the  wonders  of  other  worlds,  and 
gives  us  the  means  of  calculating  the  distances  of  the  heav- 
enly bodies,  and  of  explaining  their  phenomena  for  astro- 
nomical and  nautical  purposes. 

The  principle  of  the  telescope  will  be  readily  compre- 
hended after  what  has  been  said  concerning  the  compound 
microscope,  for  the  two  instruments  differ  chiefly  in  respect 
to  the  place  of  the  object  lens,  that  of  the  microscope  having 
a  short,  while  that  of  the  telescope  has  a  long,  focal  distance. 

713.  REFRACTING  TELESCOPE. — The  most  simple  re- 
fracting telescope  consists  of  a  tube,  containing  two  convex 
lenses,  the  one  having  a  long,  and  the  other  a  short,  focal 
distance.     (The  focal  distance  of  a  double  convex  lens,  it 
will  be  remembered,  is  nearly  the  centre  of  a  sphere,  of 
which  it  is  a  part.)     These  two  lenses  are  placed  in  the 
tube,  at  a  distance  from  each  other  equal  to  the  sum  of  their 
two  focal  distances. 

Fig.  180. 


Thus,  if  the  focus  of  the  object  glass  a,  fig.  180,  be  eight 
inches,  and  that  of  the  eye  glass  b,  two  inches,  then  the  dis- 

What  is  a  telescope  1  How  many  kinds  of  telescopes  are  mention- 
ed 1  What  is  the  difference  between  them  7  In  what  respect  does  the 
refracting  telescope  differ  from  the  compound  microscope  1  How  is 
the  most  simple  refracting  telescope  formed  1  Wh;ch  is  the  object,  and 
which  the  eye  lens,  in  fig.  180?  What  is  the  rule  by  which  the  dis- 
tance of  the  two  glasses  apart  is  found  ? 


212  TELESCOPE. 

tance  of  the  sums  of  the  foci  will  be  ten  inches,  and,  there* 
fore,  the  two  lenses  must  be  placed  ten  inches  apart ;  and 
the  same  rule  is  observed,  whatever  may  be  the  focal  lengths 
of  any  two  lenses. 

Now,  to  understand  the  effect  of  this  arrangement,  sup- 
pose the  rays  of  light,  c  d,  coming  from  a  distant  object,  as 
a  star,  to  fall  on  the  object  glass  a,  in  parallel  lines,  and  to 
be  refracted  by  the  lens  to  a  focus  at  e,  where  the  image  of 
the  star  will  be  represented.  This  image  is  then  magnified 
by  the  eye  glass  b,  and  thus,  in  effect,  is  brought  near  the 
eye. 

714.  All  that  is  effected  by  the  telescope,  therefore,  is  to 
form  an  image  of  a  distant  object,  by  means  of  the  object 
lens,  and  then  to  assist  the  eye  in  viewing  this  image  as 
nearly  as  possible  by  the  eye  lens. 

It  is,  however,  necessary  here  to  state,  that  by  the  last 
figure,  the  principle  only  of  the  telescope  is  intended  to  be 
explained,  for  in  the  common  instrument,  with  only  two 
glasses,  the  image  appears  to  the  eye  inverted. 

The  reason  of  this  will  be  aeeri  by  the  next  figure,  where 
the  direction  of  the  rays  of  light  will  show  the  position  of 
the  image. 

Fig.  181. 


Supposes,  fig.  181,  to  be  a  distinct  object,  from  which 
pencils  of  rays  flow  from  every  point  toward  the  object  lens 
b.  The  image  of  a,  in  consequence  of  the  refraction  of 
the  rays  by  the  object  lens,  is  inverted  at  c,  which  is  the  fo- 
cus of  the  eye  glass  d,  and  through  which  the  image  is  then 
seen,  still  inverted. 

715.  The  inversion  of  the  object  is  of  little  consequence 
when  the  instrument  is  employed  for  astronomical  purposes, 
for  since  the  forms  of  the  heavenly  bodies  are  spherical, 
their  positions,  in  this  respect,  do  not  affect  their  general 
appearance.  But  for  terrestrial  purposes,  this  is  manifestly  a 
great  defect,  and  therefore  those  constructed  for  such  pur- 
How  do  the  two  glasses  act,  to  bring  an  object  near  the  eyel  Ex- 
plain fig.  181,  and  show  how  the  object  comes  to  be  inverted  by  the 
two  lenses  1  H°w  is  the  inversion  of  the  object  corrected  1 


213 

poses,  as  ship,  or  spy  glasses,  have  two  additional  lenses, 
by  means  of  which,  the  images  are  made  to  appear  in  the 
same  position  as  the  objects.  These  are  called  double  tele, 
scopes. 

Fig.  182.  4**- 


Such  a  telescope  is  represented  at  fig.  182,  and  consists 
of  an  object  glass  a,  and  three  eye  glasses,  b,  c,  and  d.  The 
eye  glasses  are  placed  at  equal  distances  from  each  other,  so 
that  the  focus  of  one  may  meet  that  of  the  other,  and  thus 
the  image  formed  by  the  object  lens,  will  be  transmitted 
through  the  other  three  lenses,  to  the  eye.  The  rays  coming 
from  the  object  o,  cross  each  other  at  the  focus  of  the  object 
lens,  and  thus  form  an  inverted  image  at  /  This  image  be- 
ing also  in  the  focus  of  the  first  eye  glass,  b,  the  rays  having- 
passed  through  this  glass  become  parallel,  for,  we  have 
seen,  in  another  place,  that  diverging  rays  are  rendered  par- 
allel by  refraction  through  a  convex  lens.  The  rays,  there- 
fore, pass  parallel  to  the  next  lens  c,  by  which  they  are 
made  to  converge,  and  cross  each  other,  and  thus  the  image 
is  inverted,  and  made  to  assume  the  original  position  of  the 
object  o.  Lastly,  this  image,  being  in  the  focus  of  the  eye 
glass  d,  is  seen  in  the  natural  position,  or  in  that  of  the  ob- 
ject. 

The  apparent  magnitude  of  the  object  is  not  changed  by 
these  two  additional  glasses,  but  depends,  as  in  fig.  182,  on 
the  magnifying  power  of  the  eye  and  object  lenses;  the  two 
glasses  being  added  merely  for  the  purpose  of  making  the 
image  appear  erect. 

7l6.  It  is  found  that  an  eye  glass  of  very  high  magnify- 
ing power  cannot  be  employed  in  the  refracting  telescope, 
because  it  disperses  the  rays  of  light,  so  that  the  image  be 
:omes  indistinct.  Many  experiments  were  formerly  made 

Explain  fig.  182,  and  show  why  the  two  additional  lenses  make  the 
image  of  the  object  erect.  Does  the  addition  of  these  two  lenses  make 
*ny  difference  with  the  apparent  magnitude  of  the  object  1  Wry  can- 
not a  highly  magnifying  eye  glass  be  used  in  the  telescope"? 


214  TELESCOPE. 

with  a  view  to  obviate  this  difficulty,  and  among  these  it 
was  found  that  increasing  the  focal  distance  of  the  object 
.ens,  was  the  most  efficacious.  But  this  was  attended  with 
great  inconvenience,  and  expense,  on  account  of  the  length 
of  tube  which  this  mode  required.  These  experiments  were, 
however,  discontinued,  and  the  refracting  telescope  itself 
chiefly  laid  aside  for  astronomical  purposes,  in  consequence 
of  the  discovery  of  the  reflecting  telescope. 

717.  REFLECTING  TELESCOPE. — The  common  reflecting 
telescope  consists  of  a  large  tube,  containing  two  concave  re- 
flecting mirrors,  of  different  sizes,  and  two  eye  glasses.  The 
object  is  first  reflected  from  the  large  mirror  to  the  small 
one,  and  from  the  small  one,  through  the  two  eye  glasses, 
where  it  is  then  seen. 

718.  In  comparing  the  advantages  of  the  two   instru- 
ments, it  need  only  be  stated,  that  the  refracting  telescope, 
with  a  focal  length  of  a  thousand  feet,  if  it  could  be  used, 
would  not  magnify  distinctly  more  than  a  thousand  times, 
while  a  reflecting  telescope,  only  eight  or  nine  feet  long,  will 
magnify  with  distinctness  twelve  hundred  times. 

Fig.  183. 

r 

--P 


d       e 


719.  The  principle  and  construction  of  the  reflecting  tele- 
jcope  will  be  understood  by  fig.  183.  Suppose  the  object  o 
to  be  at  such  a  distance,  that  the  rays  of  light  from  it  pass  in 
parallel  lines,  p  p,  to  the  great  reflector  r  r.  This  reflector 
being  concave,  the  rays  are  converged  by  reflection,  and 
cross  each  other  at  a,  by  which  the  image  is  inverted.  The 
rays  then  pass  to  the  small  mirror,  bt  which  being  also  con- 
cave, they  are  thrown  back  in  nearly  parallel  lines,  and 
having  passed  the  aperture  in  the  centre  of  the  great  mirror, 
fall  on  the  plano-convex  lens  e.  By  this  lens  they  are  re- 

What  is  the  most  efficacious  means  of  increasing  the  power  of  the 
refracting  telescope  1  How  many  lenses  and  mirrors  form  the  reflect- 
ing telescope  1  What  are  the  advantages  of  the  reflecting  over  the  re- 
fracting telescope?  Explain  fig.  183,  and  show  the  course  of  the  rays 
from  the  object  to  the  eye. 


TELESCOPE.  215 

fracted  to  a  focus,  and  cross  each  other  between  e  and  d,  and 
thus  the  image  is  again  inverted,  and  brought  to  its  original 
position,  or  in  the  position  of  the  object.  The  rays  then, 
passing  the  second  eye  glass,  form  the  image  of  the  object 
on  the  retina. 

The  large  mirror  in  this  instrument  is  fixed,  but  the  small 
one  moves  backwards  and  forwards,  by  means  of  a  screw, 
so  as  to  adjust  the  image  to  the  eyes  of  different  persons. 
Both  mirrors  are  made  of  a  composition,  consisting  of  sev- 
eral metals  melted  together. 

720.  One  great  advantage  which  the  reflecting  telescope 
possesses  over  the  refracting,  appears  to  b^  that  it  admits  of 
an  eye  glass  of  shorter  focal  distance,  and,  consequently,  of 
greater  magnifying  power.     The  convex  object  glass  of  the 
refracting  instrument,  does  not  form  a  perfect  image  of  the 
object,  since  some  of  the  rays  are  dispersed,  and  others  co- 
loured by  refraction.     This  difficulty  does  not  occur  in  the 
reflected  image  from  the  metallic  mirror  of  the  reflecting 
telescope,  and  consequently  it  may  be  distinctly  seen,  when 
more  highly  magnified. 

The  instrument  just  described  is  called  "  Gregory's  tele- 
scope" because  some  parts  of  the  arrangement  were  invent- 
ed by  Dr.  Gregory. 

721.  In  the  telescope  made  by  Dr.  Herschel, the  object' s 
reflected  by  a  mirror,  as  in  that  of  Dr.  Gregory.     But  the 
second,  or  small  reflector,  is  not  employed,  the  image  being- 
seen  through  a  convex  lens,  placed  so  as  to   magnify  the 
linage  of  the  large  mirror,  so  that  the  observer  stands  with 
his  back  towards  the  object. 

The  magnifying  power  of  this  instrument  is  the  same  as 
that  of  Dr.  Gregory's,  but  the  image  appears  brighter,  be- 
cause there  is  no  second  reflection  ;  for  every  reflection  ren- 
ders the  image  fiinter,  since  no  mirror  is  so  perfect  as  to 
throw  back  all  the  rays  which  fall  upon  its  surface. 

722.  In  Dr.  Herschel's  grand  telescope,  the  largest  ever 
constructed,  the  reflector  was  48   inches  in  diameter,  and 
had  a  focal  distance  of  40  feet.     This  reflector  was  three 
and  a  half  inches  thick,  and  weighed  2000  pounds.     Now, 
since  the  focus  of  a  concave  mirror  is  at  the  distance  of  one 

Why  is  the  small  mirror  in  this  instrument  made  to  move  by  means 
of  a  screw]  What  is  the  advantage  of  the  reflecting  telescope  in  re- 
spect to  the  eye  glass  1  Why  is  the  telescope  with  two  reflectors  called 
Gregory's  telescope  1  How  does  this  instrument  differ  from  Dr.  Her- 
schel's telescope  7  What  was  the  focal  distance  and  diameter  of  the 
mirror  in  Dr.  Herschel's  great  telescope? 


CAMERA  QBSCURA. 

half  the  semi-diameter  of  the  sphere,  of  which  it  is  a  section 
DJ.  Herschel's  reflector  having  a  focal  distance  of  40  feev, 
formed  a  part  of  a  sphere  of  160  feet  in  diameter. 

This  great  instrument  was  begun  in  1785,  and  finished 
four  years  afterwards.  The  frame  by  which  this  wonder 
to  all  astronomers  was  supported,  having  decayed,  it  was 
taken  down  in  1822,  and  another  of  20  feet  focus,  with  a 
reflector  of  18  inches  in  diameter,  erected  in  its  place,  by 
Herschel's  son. 

The  largest  Herschel's  telescope  now  in  existence  is  that 
of  Greenwich  observatory,  in  England.  This  has  a  con- 
cave reflector  of  15  inches  in  diameter,  with  a  focal  length 
of  25  feet,  and  was  erected  in  1820. 

723.  CAMERA  OBSCURA. — Camera  obscura  strictly  signi- 
fies a  darkened  chamber,  because  the  room  must  be  dark- 
ened, in  order  to  observe  its  effects. 

To  witness  the  phenomena  of  this  instrument,  let  a  room 
be  closed  in  every  direction,  so  as  to  exclude  the  light. 
Then  from  an  aperture,  say  of  an  inch  in  diameter,  admit  a 
single  beam  of  light,  and  the  images  of  external  things,  such 
as  trees,  and  houses,  and  persons  walking  the  streets,  will  be 
seen  inverted  on  the  wall  opposite  to  where  the  light  is  admit- 
ted, or  on  a  screen  of  white  paper,  placed  before  the  aperture. 

724.  The  reason  why  the  image  is  inverted,  will  be  ob- 
vious, when  it  is  remembered  that  the  rays  proceeding  from 
the  extremities  of  the  object  must  converge  in  order  to  pass 
through  the  small  aperture ;  and  as  the  rays  of  light  always 
proceed  in  straight  lines,  they  must  cross  each  other  at  the 
point  of  admission,  as  expjained  under  the  article  Vision. 

Thus,     the  Fig.  184. 

pencil  a,  fig. 
184,  coming 
from  the  up- 
per part  of  the 
tower,  and 
proceeding 
straight,  will 
represent  the 
image  of  that 
part  at  b,  while 
the  lower  part 

Where  is  the  largest  Herschel's  telescope  now  in  existence  ?  What 
is  the  diameter  and  focal  distance  of  the  reflector  of  this  telescope'? 
Describe  the  phenomena  of  the  camera  obscura.  Why  is  the  image 
formed  by  the  camera  obscura  inverted  1 


MAGIC  LANTERN. 


217 


Fig.  185. 


c,  for  the  same  reason  will  be  represented  at  d.  If  a  con- 
vex lens,  with  a  short  tube,  be  placed  in  the  aperture 
through  which  the  light  passes  into  the  room,  the  images 
of  things  will  be  much  more  perfect,  and  their  colours  more 
brilliant. 

725.  This    instrument    is 
sometimes  employed  by  paint- 
ers, in  order  to  obtain  an  exact 
delineation  of  a  landscape,  an 
outline  of  the  image  being  ea- 
sily taken  with  a  pencil,  when 
the  image  is  thrown  on  a  sheet 
of  paper. 

There  are  several  modifica- 
tions of  this  machine,  and 
among  them  the  revolving  ca- 
mera obscura  is  the  most  in- 
teresting. 

It  consists  of  a  small  house, 
fig.  185,  with  a  plane  reflect-*? 
or,  a  b,  and  a  convex  lens,  c  b, 
placed  at  its  top.  The  reflect- 
or is  fixed  at  an  angle  of  45  degrees  with  the  horizon,  so  as 
to  reflect  the  rays  of  light  perpendicularly  downwards,  and 
is  made  to  revolve  quite  around,  in  either  direction,  by 
pulling  a  string. 

Now  suppose  the  small  house  to  be  placed  in  the  open 
air,  with  the  mirror,  a  b,  turned  towards  the  east,  then  the 
rays  of  light  flowing  from  the  objects  in  that  direction,  will 
strike  the  mirror  in  the  direction  of  the  lines  o,  and  be  re- 
flected down  through  the  convex  lens  c  b,  to  the  table  e  e, 
where  they  will  form  in  miniature  a  most  perfect  and  beau- 
tiful picture  of  the  landscape  in  that  direction.  Then,  by 
making  the  reflector  revolve,  another  portion  of  the  land- 
scape may  be  seen,  and  thus  the  objects,  in  all  directions, 
can  be  viewed  at  k  without  changing  the  place  of  the  in- 
strument. 

726.  MAGIC  LANTERN. — The  Magic  Lantern  is  a  mi- 
croscope, on  the  same  principle  as  the  solar  microscope. 
But  instead  of  being  used  to  magnify  natural  objects,  it  is 
t-ommonly  employed  for  amusement,  by  the  casting  shadows 

How  may  an  outline  of  the  image  formed  by  the  camera  obscura  be 
taken?  Describe  the  revolving  camera  obscura.  What  is  the  magic 
lantern  1  For  what  purpose  is  this  instrument  employed? 

19 


218  CHROMATICS. 

of  small  transparent  paintings  done  on  glass,  upon  a  screen 
placed  at  a  proper  distance. 

Fig.  186. 


o   n 


Let  a  candle  c,  fig.  186,  be  placed  on  the  inside  of  a  box, 
or  tube,  so  th^t  its  light  may  pass  through  the  plano-convex 
lens  n,  and  strongly  illuminate  the  object  o.  This  object  is 
generally  a  small  transparent  painting  on  a  slip  of  glass, 
which  slides  through  an  opening  in  the  tube.  In  order  to 
show  the  figures  in  the  erect  position,  these  paintings  are  in- 
verted, since  their  shadows  are  again  inverted  by  the  refrac- 
tion of  the  convex  lens  m. 

In  some  of  these  instruments,  there  is  a  concave  mirror, 
dy  by  which  the  object,  o,  is  more  strongly  illuminated  than 
it  would  be  by  the  lamp  alone.  The  object  is  magnified  by 
the  double  convex  lens,  m,  which  is  moveable  in  the  tube  by 
a  screw,  so  that  its  focus  can  be  adjusted  to  the  required  dis- 
tance. Lastly,  there  is  a  screen  of  white  cloth,  placed  at 
the  proper  distance,  on  which  the  image,  or  shadow  of  the 
picture,  is  seen  greatly  magnified. 

The  pictures  being*  of  various  colours,  and  so  transparent, 
that  the  light  of  the  lamp  shines  through  them,  the  shadows 
are  also  of  various  colours,  and  thus  soldiers  and  horsemen 
are  represented  in  their  proper  costume. 

CHROMATICS,  OR  THE  PHILOSOPHY  OF  COLOURS. 

727.  We  have  thus  far  considered  light  as  a  simple  sub- 
stance, and  have  supposed  that  all  its  parts  were  equally  re 
fracted,  in  its  passage  through  the  several  lenses  described. 
But  it  will  now  be  shown  that  light  is  a  compound  body, 
and  that  each  of  its  rays,  which  to  us  appear  white,  is  corn- 
Describe  the  construction  and  effect  of  the  magic  lantern. 


CHROMATICS. 


219 


posed  of  several  colours,  and  that  each  colour  suffers  a  dif- 
ferent degree  of  refraction,  when  the  rays  of  light  pass 
through  a  piece  of  glass,  of  a  certain  shape. 

728.  The  discovery,  that  light  is  a  compound  substance, 
and  that  it  may  be  decomposed,  or  separated  into  parts,  was 
made  by  Sir  Isaac  Newton. 

If  a  ray,  proceeding  from  the  sun,  be  admitted  into  a 
darkened  chamber,  through  an  aperture  in  the  window  shut- 
ter, and  allowed  to  pass  through  a  triangular  shaped  piece 
of  glass,  called  a  prism,  the  light  will  be  decomposed,  and- 
instead  of  a  spot  of  white  light,  there  will  be  seen,  on  the 
opposite  wall,  a  most  brilliant  display  of  colours,  including 
all  those  which  are  seen  in  the  rainbow. 
Fig.  187. 


Suppose  s,  fig.  187,  to  be  a  ray  from  the  sun,  admitted 
through  the  window  shutter  a,  in  such  a  direction  as  to  fall 
on  the  floor  at  c,  where  it  would  form  a  round,  white  spot. 
Now,  on  interposing  the  prism  p,  the  ray  will  be  refracted, 
and  at  the  same  time  decomposed,  and  will  form  on  the 
screen  m,  n,  an  oblong  figure,  containing  seven  colours, 
which  will  be  situated  in  respect  to  each  other,  as  named  in 
the  figure. 

It  may  be  observed,  that  of  all  the  colours,  the  red  is  least 
refracted,  or  is  thrown  the  smallest  distance  from  the  direc 
tion  of  the  original  sun  beam,  and  that  the  violet  is  most  re 
fracted,  or  bent  out  of  that  direction. 

The  oblong  image  containing  the  coloured  rays,  is  called 
the  solar  or  prismatic  spectrum. 

729.  That  the  rays  of  the  sun  are  composed  of  the  seven 

Who  made  the  discovery,  that  light  is  a  compound  substance"?  In 
what  manner,  and  by  what  means,  is  light  decomposed?  What  are 
the  prismatic  colours,  and  how  do  they  succeed  each  other  in  the  spec- 
trum ?  Which  colour  is  refracted  most,  and  which  least  *? 


220  CHROMATICS. 

colours  above  named,  is  sufficiently  evident  by  the  fact,  that 
such  a  ray  is  divided  into  these  several  colours  by  passing- 
through  the  prism,  but  in  addition  to  this  proof,  it  is  found 
by  experiment,  that  if  these  several  colours  be  blended  or 
mixed  together,  white  will  be  the  result. 

This  may  be  done  by  mixing  together  seven  powders, 
whose  colours  represent  the  prismatic  colours,  and  whose 
quantities  are  to  each  other,  as  the  spaces  occupied  by  each 
colour  in  the  spectrum.  When  this  is  done,  it  will  be  found 
that  the  resulting  colour  will  be  a  grayish  white.  A  still 
more  satisfactory  proof  that  these  seven  colours  form  white, 
when  united,  is  obtained  by  causing  the  solar  spectrum  to 
pass  through  a  lens,  by  which  they  are  brought  to  a  focus, 
when  it  is  found  that  the  focus  will  be  the  same  colour  as  il 
would  be  from  the  original  rays  of  the  sun. 

730.  From  the  oblong  shape  of  the  solar  spectrum,  we 
learn  that  each  of  the  coloured  rays  is  refracted  in  a  differ- 
ent degree  by  passing  through  the  same  medium,  and  con- 
sequently that  each  ray  has  a  refractive  power  of  its  own. 
Thus,  from  the  red  to  the  violet,  each  ray,  in  succession,  is 
refracted  more  than  the  other. 

731.  The  prism  is  not  the  only  instrument  by  which 
light  can  be  decomposed.     A  soap  bubble  blown  up  in  the 
sun  will  display  most  of  the  prismatic  colours.     This  is  ac- 
counted for  by  supposing  that  the  sides  of  the  bubble  vary  in 
thickness,  and  that  the  rays  of  light  are  decomposed  by  these 
variations.     The  unequal  surface  of  mother  of  pearl,  and 
many  other  shells,  send  forth  coloured  rays  on  the  same 
principle. 

732.  Two  surfaces  of  polished  glass,  when  pressed  to- 
gether, will  also  decompose  the  light.     Rings  of  coloured 
light  will  be  observed  around  the  point  of  contact  between 
the  two  surfaces,  and  their  number  may  be  increased  CT  di- 
minished by  the  degrees  of  pressure.     Two  pieces  of  com- 
mon looking  glass,  pressed  together  with  the  fingers,  will 
display  most  of  the  prismatic  colours. 

733.  A  variety  of  substances,  when  thrown  into  the  form 
of  the  triangular  prism,  will  decompose  the  rays  of  light, 

When  the  several  prismatic  colours  are  blended,  what  colour  is  the 
result  ?  When  the  solar  spectrum  is  made  to  pass  through  a  lens,  what 
is  the  colour  of  the  focus  1  How  do  we  learn  that  each  coloured  ray 
has  a  refractive  power  of  its  own  ?  By  what  other  means  besides  the 
prism,  can  the  rays  of  light  be  decomposed'?  How  may  light  be  de- 
composed by  two  pieces  of  glass  1  Of  what  substances  may  prisms  be 
formed,  besides  glass  T 


RAINBOW.  221 

is  well  as  a  prism  of  glass.  A  very  common  instrument 
for  this  purpose  is  made  by  putting  together  three  pieces  of 
plate  glass,  in  form  of  a  prism.  The  ends  may  be  made 
of  wood,  and  the  edges  cemented  with  putty,  so  as  to  make 
the  whole  water  tight.  When  this  is  filled  with  water,  and 
held  before  a  sun  beam,  the  solar  spectrum  will  be  formed, 
displaying  the  same  colours,  and  in  the  same  order,  as  that 
above  described. 

734.  In  making  experiments  with  prisms,  filled  with  dif- 
ferent kinds  of  liquids,  it  has  been  found  that  one  liquid  will 
make  the  spectrum J  mger  than  another ;  that  is,  the  red  and 
violet  rays,  which  form  the  extremes  of  the  spectrum,  will 
be  thrown  farther  apart  by  one  fluid,  than  by  another.    For 
example,  if  the  prism  be  filled  with  oil  of  cassia,  the  spec- 
trum formed  by  it,  will  be  more  than  twice  as  long  as  that 
formed  by  a  prism  of  solid  glass.    The  oil  of  cassia  is  there- 
fore said  to  disperse  the  rays  of  light  more  than  glass,  and 
hence  to  have  a  greater  dispersive  power. 

735.  THE  RAINBOW. — The  rainbow  was  a  phenomenon, 
for  which  the  ancients  were  entirely  unable  to  account ;  but 
after  the  discovery  that  light  is  a  compound  principle,  and 
that   its  colours  may  be  separated   by  various  substances, 
the  solution  of  this  phenomenon  became  easy. 

Sir  Isaac  Newton,  after  his  great  discovery  of  the  com- 
pound nature  of  light,  and  the  different  refrangibility  of  the 
coloured  rays,  was  able  to  explain  the  rainbow  on  optical 
principles. 

736.  If  a  glass  globe  be  suspended  in  a  room,  where  the 
rays  of  the  sun  can  fall  upon  it,  the  light  will  be  decom- 
posed, or  separated  into  several  coloured  rays,  in  the  same 
manner  as  is  done  by  the  prism.     A  well  defined  spectrum 
will  not,  however,  be  formed  by  the  globe,  because  its  shape 
is  such  as  to  disperse  some  of  the  rays,  and  converge  others; 
but  the  eye,  by  taking  different  positions  in  respect  to  the 
globe,  will  observe  the  various  prismatic  colours.     Trans- 
parent bodies,  such  as  glass  and  water,  reflect  the  rays  of 
light  from  both  their  surfaces,  but  chiefly  from  the  second 
surface.     That  is,  if  a  plate  of  naked  glass  be  placed  so  as 
to  reflect  the  image  of  the  sun,  or  of  a  lamp,  to  the  eye,  the 

What  is  said  of  some  liquids  making  the  spectrum  larger  than  oth- 
ers 1  What  is  said  of  oil  of  cassia,  in  this  respect  1  What  discovery 
oreceded  the  explanation  of  the  rainbow  1  Who  first  explained  the 
rainbow  on  optical  principles  7  Why  do*:s  not  a  glass  globe  form  a 
well  defined  spectrum  '1  From  which  surface  do  transparent  bodies 
chiefly  reflect  the  light  ? 

19* 


222  RAINBOW. 

most  distinct  image  will  come  from  the  second  surface,  01 
that  most  distant  from  the  eye.  The  great  brilliancy  of  the 
diamond  is  owing  to  this  cause.  It  will  be  understood  di- 
rectly, how  this  principle  applies  to  the  explanation  of  the 
jainbow. 

Suppose  the  circle  a  b  c,  fig.  188,  to  represent  a  globe,  or 
a  drop  of  rain,  for  each  drop  of  rain,  as  it  falls  through  the 
air,  is  a  small  Fig.  188. 

globe  of  water. 
Suppose,  also, 
that  the  sun  is 
at  s,  and  the  eye 
of  the  spectator 
at  e.  Now,  it 
has  already 
been  stated,  that 
from  a  single 
globe,  the 

whole  solar 
spectrum  is  not 
seen  in  the  same  position,  but  that  the  different  colours  are 
seen  from  different  places.  Suppose,  then,  that  a  ray  of 
light  from  the  sun  s,  on  entering  the  globe  at  a,  is  separated 
into  its  primary  colours,  and  at  the  same  time  the  red  ray, 
which  is  the  least  refrangible,  is  refracted  in  the  line  from 
a  to  b.  From  the  second,  or  inner  surface  of  the  globe,  it 
would  be  reflected  to  c,  the  angle  of  reflection  being  equal 
to  that  of  incidence.  On  passing  out  of  the  globe,  its  re- 
fraction at  c,  would  be  just  equal  to  the  refraction  of  the  in- 
cident ray  at  a,  and  therefore  the  red  ray  would  fall  on  the 
eye  at  e.  All  the  other  coloured  rays  would  follow  the 
same  law,  but  because  the  angles  of  incidence  and  those  of 
reflection  are  equal,  and  because  the  colored  rays  are  separa- 
ted from  each  other  by  unequal  refraction,  it  is  obvious,  that 
if  the  red  ray  entered  the  eye  at  e,  none  of  the  other  coloured 
rays  could  be  seen  from  the  same  point. 

737.  From  this  it  is  evident,  that  if  the  eye  of  the  spec- 
tator is  moved  to  another  position,  he  will  not  see  the  red  ray 
coming  from  the  same  drop  of  rain,  but  only  the  blue,  and 
if  to  another  position,  the  green,  and  so  of  all  the  others. 

Explain  fig.  188,  and  show  the  different  refractions,  and  the  reflection 
concerned  in  forming  the  rainbow.  In  the  case  supposed,  why  will 
only  the  red  ray  meet  the  eye!  Suppose  a  person  looking  at  a  rain- 
bow moves  his  eye,  will  he  see  the  same  colours  from  the  same  drop 
of  rain  ? 


RAINBOW. 


223 


But  m  a  shower  of  rain,  there  are  drops  at  all  heights  and 
distances,  and  though  they  perpetually  change  their  places, 
in  respect  to  the  sun  and  the  eye,  as  they  fall,  still  there  will 
be  many  which  will  be  in  such  a  position  as  to  reflect  the 
red  rays  to  the  eye,  and  as  many  more  to  reflect  the  yellow 
rays,  and  so  of  all  the  other  colours. 

This    will    be  Fig.  189 

made  obvious  by 
fig.  189,  where, 
to  avoid  confu- 
sion, we  will  sup- 
pose that  only 
three  drops  of 
rain,  and,  con- 
sequently, only 
three  colours,  are 
to  be  seen. 

The  numbers 
1,  2,  3,  are  the 
rays  of  the  sun, 
proceeding  to  the 
drops  a,  b,  c,  and 
from  which  these 
rays  are  reflect- 
ed to  the  eye,  ma- 
king different  angles  with  the  horizontal  line  A,  because  one 
coloured  ray  is  refracted  more  than  another.  Now,  suppose 
the  red  ray  only  reaches  the  eye  from  the  drop  a,  the  green 
from  the  drop  b,  and  the  violet  from  the  drop  c,  then  the 
spectator  would  see  a  minute  rainbow  of  three  colours.  But 
during  a  shower  of  rain,  all  the  drops  which  are  in  the  po- 
sition of  a,  in  respect  to  the  eye,  would  send  forth  red  rays, 
and  no  other,  while  those  in  the  position  of  b,  would  emit 
green  rays,  and  no  other,  and  those  in  the  position  of  c,  vio- 
let rays,  and  so  of  all  the  other  prismatic  colours.  Each 
circle  of  colours,  of  which  the  rainbow  is  formed,  is  there- 
fore composed  of  reflections  from  a  vast  number  of  differ- 
ent drops  of  rain,  and  the  reason  why  these  colours  are  dis- 
tinct to  our  senses,  is,  that  we  see  only  one  colour  from  a 
single  drop,  with  the  eye  in  the  same  position.  It  follows, 
then,  that  if  we  change  our  position,  while  looking  at  a 

Explain  fig.  189,  and  show  why  we  see  different  colours  from  differ- 
ent drops  of  rain.  Do  several  persons  see  the  same  rainbow  at  the 
same  time  1 


224 


RAINBOW, 


rainbow,  we  still  see  a  bow,  but  not  the  same  as  before,  and 
hence,  if  there  are  many  spectators,  they  will  all  see  a  differ- 
ent rainbow,  though  it  appears  to  be  the  same. 

738.  There  are  often  seen  two  rainbows,  the  one  formed 
as  above  described,  and  the  other,  which  is  fainter,  appear- 
ing on  the  outside,  or  above  this.     The  secondary  bow,  as 
this  last  is  called,  always  has  its  order  of  colours  the  reverse 
of  the  primary  one.     Thus,  the  colours  of  the  primary  bow, 
beginning  with  its  upper,  or  outermost  portion,  are  red, 
orange,  yellow,  &c.,  the  lowest,  or  innermost  portion,  being 
violet;  while  the  secondary  bow,  beginning  with  the  same 
corresponding  part,  is  coloured  violet,  indigo,  &c.,  the  low- 
est, or  innermost  circle,  being  red. 

739.  In  the  primary  bo\v,  we  have  seen,  that  the  coloured 
rays  arrive  at  the  eye  after  two  refractions,  and  one  reflec- 
tion.    In  the  secondary  bo\v,  the  rays  reach  the  eye  after 
two  refractions,  and  two  reflections,  and  the  order  of  the 
colours  is  reversed,  because,  in  this  case,  the  rays  of  light 
enter  the  lower  part  of  the  drop,  instead  of  the  upper  part, 
as  in  the  primary  bow.     The  reason  why  the  colours  are 
fainter  in  the  secondary  than  in  the  primary  bow  is,  because 
a  part  of  the  light  is  lost  or  dispersed,  at  each  reflection, 
and  there  being  two  reflections,  by  which  this  bow  is  form- 
ed, instead  of  one,  as  in  the  primary,  the  difference  in  bril- 
liancy is  very  obvious. 

740.  The  direction  of  a  single  ray,  showing  how  the 
secondary  bow  is  formed,  will  be  seen  at  fig.  190.   The  ray 
r,  from  the  Fig.  190. 

sun,  enters 
the  drop  of 
water  at  a, 
and  is  re- 
fracted to 

c,  then  re- 
flected to  b, 
then  again 
reflected  to 

d,  where  it 
suffers   an- 
other     re- 

fraction,  and  lastly,  passes  to  the  eye  of  the  Spectator  at  e. 

Explain  the  reason  of  this.  How  are  the  colours  of  the  primary 
and  secondary  bows  arranged  in  respect  to  each  other  1  How  many 
refractions  and  reflections  produce  the  secondary  bow  1  Why  is  the 
secondary  bow  less  brilliant  than  the  primary  ? 


COLOURS.  225 

The  rainbow,  being  the  consequence  of  the  refracted  and 
reflected  rays  of  the  sun,  is  never  seen,  except  when  the 
sun  and  the  spectator  are  in  similar  directions,  in  respect  to 
the  shower.  It  assumes  the  form  of  a  semicircle,  because 
it  is  only  at  certain  angles  that  the  refracted  rays  are  visible 
to  the  eye. 

741.  Of  the  colours  of  things.     The  light  of  the  sun,  we 
have  seen,  may  be  separated  into  seven  primary  rays,  each 
of  which  has  a  colour  of  its  own,  and  which  is  different 
from  that  of  the  others.     In  the  objects  which  surround  us, 
both  natural  and  artificial,  we  observe  a  great  variety  of 
colours,   which   differ    from    those    composing  the   solar 
spectrum,  and  hence  one  might  be  led  to  believe  that  both 
nature  and  art  afford  colours  different  from  those  afforded 
by  the  decomposition  of  the   solar   rays.     But  it  must  be 
remembered,   that   the   solar   spectrum  contains   only   the 
primary  colours  of  nature,  and  that  by  mixing  these  colours 
in  various  proportions  with  each  other,  an  indefinite  variety 
of  tints,  all  differing  from  their  primaries,  may  be  obtained. 

742.  It  appears  that  the  colours  of  all  bodies  depend  on 
some  peculiar  property  of  their  surfaces,  in  consequence  of 
which,  they  absorb  some  of  the  coloured  rays,  and  reflect  the 
others.     Had  the  surfaces  of  all  bodies  the  property  of  re- 
flecting the  same  ray  only,  all  nature  would  display  the 
monotony  of  a  single  colour,  and  our  senses  would  never 
have  known  the  charms  of  that  variety  which  we  now 
behold. 

743.  All  bodies  appear  of  the  colour  of  that  ray,  or  of  a 
tint  depending  on  the  several  rays  which  it  reflects,  while 
all  the  other  rays  are  absorbed,  or,  in  other  terms,  are  not 
reflected.     Black  and  white,  therefore,  in  a  philosophical 
sense,  cannot  be  considered  as  colours,  since  the  first  arises 
from  the  absorption  of  all  the  rays,  and  the  reflection  of 
none,  and  the  last  is  produced  by  the  reflection  of  all  the 
rays,  and  the  absorption  of  none.     But  in  all  colours,  or 
shades  of  colour,  the  rays  only  are  reflected,  of  which  the 
colour  is  composed.  Thus,  the  colour  of  grass,  and  the  leaves 
of  plants,  is  green,  because  the  surfaces  of  these  substances 
reflect  only  the  green  rays,  and  absorb  all  the  others.     For 

Why  are  the  colours  of  things  different  from  those  of  the  solar  spec- 
trum 1  On  what  do  the  colours  of  bodies  depend  1  Suppose  all  bodies 
reflected  the  same  ray,  what  would  be  the  consequence,  in  regard  to 
colour  1  Why  are  not  black,  and  white,  considered  as  colours  1  Why 
is  the  colour  of  grass  green"? 


226  COLOURS. 

the  same  reason,  the  rose  is  red,  the  violet  blue,  and  so  of  all 
coloured  substances,  every  one  throwing  out  the  ray  of  its 
own  colour,  and  absorbing  all  the  others. 

744.  To  account  for  such  a  variety  of  colours  as  we  see  in 
different  bodies,  it  is  supposed  that  all  substances,  when  made 
sufficiently  thin,  are   transparent,    and   consequently,  that 
they  transmit  through  their  surfaces,  or  absorb,  certain  rays 
of  light,  while  other  rays  are  thrown  back,  or  reflected,  as 
above  described.     Gold,  for  example,  may  be  beat  so  thin  as 
to  transmit  some  of  the  rays  of  light,  and  the  same  is  true  of 
several  of  the  other  metals,  which  are  capable  of  being  ham- 
mered into  thin  leaves.     It  is  therefore  most  probable,  that 
all  the  metals,  could  they  be  made  sufficiently  thin,  would 
permit  the  rays  of  light  to  pass  through  them.     Most,  if  not 
quite  all  mineral  substances,  though  in  the  mass  they  may 
seem  quite  opaque,  admit  the  light  through  their  edges,  when 
broken,  and  almost  every  kind  of  wood,  when  made  no  thinner 
than  writing  paper,  becomes  translucent.    Thus  we  may  safe- 
ly conclude,  that  every  substance  with  which  we  are  ac- 
quainted, will  admit  the  rays  of  light,  when  made  sufficiently 
thin. 

745.  Transparent  colourless  substances,  whether  solid  or 
fluid,  such  as  glass,  water,  or  mica,  reflect  and  transmit  light 
of  the  same  colour ;  that  is,  the  light  seen  through  these 
bodies,  and  reflected  from  their  surfaces,  is  white,     This  is 
true  of  all  transparent  substances  under  ordinary  circum- 
stances; but  if  their  thickness  be  diminished  to  a  certain 
extent,   these    substances   will    both    reflect   and   transmit 
coloured  light  of  various  hues,  according  to  their  thickness. 
Thus,  the  thin  plates  of  mica,  which  are  left  on  the  fingers, 
after  handling  that  substance,  will  reflect  prismatic  rays  of 
various  colours. 

746.  There  is  a  degree  of  tenuity,  at  which  transparent 
substances  cease  to  reflect  any  of  the  coloured  rays,  but 
absorb,  or  transmit  them  all,  in  which  case  they  become 
black.     This  may  be  proved  by  various  experiments.     If  a 
soap  bubble  be  closely  observed,  it  will  be  seen  that  at  first, 
the  thickness  is  sufficient  to  reflect  the  prismatic  rays  from 

How  is  the  variety  of  colours  accounted  for,  by  considering  all 
bodies  transparent  ?  What  is  said  of  the  reflection  of  coloured  light  by 
transparent  substances  1  What  substance  is  mentioned,  as  illustrating 
this  fact  ?  When  is  it  said  that  transparent  substances  become  black  7 
How  is  it  proved  that  fluids  of  extreme  tenuity  absorb  all  the  rays  and 
reflect  none  ? 


COLOURS.  227 

all  its  parts,  but  as  it  grows  thinner,  and  just  before  it 
bursts,  there  may  be  seen  a  spot  on  its  top,  which  turns 
black,  thus  transmitting  all  the  rays  at  that  part,  and  re- 
flecting none.  The  same  phenomenon  is  exhibited,  when 
a  film  of  air,  or  water,  is  pressed  between  two  plates  of 
glass.  At  the  point  of  contact,  or  where  the  two  plates 
press  each  other  with  the  greatest  force,  there  will  be  a 
black  spot,  while  around  this  there  may  be  seen  a  system 
of  coloured  rings. 

From  such  experiments,  Sir  Isaac  Newton  concluded, 
that  air,  when  below  the  thickness  of  half  a  millionth  of 
an  inch,  ceases  to  reflect  light ;  and  also  that  water,  when 
below  the  thickness  of  three  eighths  of  a  millionth  of  an 
inch,  ceases  to  reflect  light.  But  that  both  air  and  water, 
Avhen  their  thickness  is  in  a  certain  degree  above  these 
limits,  reflect  all  the  coloured  rays  of  the  spectrum. 

747.  Now  all  solid  bodies  are  more  or  less  porous,  having 
among  their  particles  either  void  spaces,  or  spaces  filled 
with  some  foreign  matter,  differing  in  density  from  the  body 
itself,  such  as  air  or  water.    Even  gold  is  not  perfectly  com- 
pact, since  water  can  be  forced  through  its  pores.     It  is 
most  probable,  then,  that  the  parts  of  the  same  body,  differ- 
ing in  density,  either  reflect,  or  transmit  the  rays  of  light, 
according  to  the  size  or  arrangement  of  their  particles ; 
and  in  proof  of  this,  it  is  found  that  some  bodies  transmit 
the  rays  of  one  colour,  and  reflect  that  of  another.     Thus, 
the  colour  which  passes  through  a  leaf  of  gold  is  green, 
while  that  which  it  reflects  is  yellow. 

748.  From  a  great  variety  of  experiments  on  this  sub- 
ject, Sir  Isaac  Newton  concludes  that  the  transparent  parts 
of  bodies,  according  to  the  sizes  of  their  transparent  pores, 
reflect  rays  of  one  colour,  and  transmit  those  of  another, 
for  the  same  reason  that  thin  plates,  or  minute  particles  of 
air,  water,  and  some  other  substances,  reflect  certain  rays, 
and  absorb,  or  transmit  others,  and  that  this  is  the  cause  of 
all  their  colours. 

749.  In  confirmation  of  the  truth  of  this  theory,  it  may 
be  observed,  that  many  substances,  otherwise  opaque,  become 
transparent,  by  filling  their  pores  with  some  transparent 
fluid. 


"What  is  the  conclusion  of  Sir  Isaac  Newton,  concerning  the  tenuity 
at  which  water  and  air  ceases  to  reflect  light  1  What  is  said  of  the 
porous  nature  of  the  solid  bodies  ? 


228  ASTRONOMY. 

Thus,  the  stone  called  Hydrophane,  is  perfectly  opaque 
when  dry,  but  becomes  transparent  when  dipped  in  uater; 
and  common  writing  paper  becomes  translucent,  after  it  has 
absorbed  a  quantity  of  oil.  The  transparency,  in  these  cases, 
may  be  accounted  for,  by  the  different  refractive  powers 
which  the  water  and  oil  possess,  from  the  stone  or  paper,  and 
in  consequence  of  which  the  light  is  enabled  to  pass  among 
their  particles  by  refraction. 


ASTRONOMY. 

750.  Astronomy  is  that  science  which  treats  of  the  mo 
tions  and  appearances  of  the  heavenly  bodies ;  accounts  for 
the  phenomena  which  these  bodies  exhibit  to  us ;  and  explains 
the  laws  by  which  their  motions,  or  apparent  motions,  are 
regulated. 

Astronomy  is  divided  into  Descriptive,  Physical,  and 
Practical. 

Descriptive  astronomy  demonstrates  the  magnitudes,  dis- 
tances, and  densities  of  the  heavenly  bodies,  and  explains  the 
phenomena  dependant  on  their  motions,  such  as  the  change 
of  seasons,  and  the  vicissitudes  of  day  and  night. 

Physical  astronomy  explains  the  theory  of  planetary 
motion,  and  the  laws  by  which  this  motion  is  regulated  and 
sustained. 

Practical  astronomy  details  the  description  and  use  ot  :is 
tronomical  instruments,  and  develops  the  nature  and  appli- 
cation of  astronomical  calculations. 

The  heavenly  bodies  are  divided  into  three  distinct  classes, 
or  systems,  namely,  the  solar  system,  consisting  of  the  sun, 
moon,  and  planets,  the  system  of  the  fixed  stars,  and  the 
system  of  the  comets. 

THE  SOLAR  SYSTEM. 

751.  The  Solar  System  consists  of  the  sun,  and  twenty- 
nine  other  bodies,  which  revolve  around  him  at  various  dis- 
tances, and  in  various  periods  of  time. 

The  bodies  which  revolve  around  the  sun  as  a  centre,  are 

What  is  astronomy  ?  How  is  astronomy  divided  1  What  does  des- 
criptive astronomy  teach  1  What  is  the  object  of  physical  astronomy  1 
What  is  practical  astronomy  1  How  are  the  heavenly  bodies  divided  1 
Of  what  does  the  solar  system  consist  1  What  are  the  bodies  called, 
which  revolve  around  the  sun  as  a  centre  7 


ASTRONOMY,  229 

called  primary  planets.  Thus,  the  Earth,  Venus,  and  Mars, 
are  primary  planets.  Those  which  revolve  around  the  pri- 
mary planets,  are  called  secondary  planets,  moons,  or  satel- 
lites. Our  moon  is  a  secondary  planet  or  satellite. 

The  primary  planets  revolve  around  the  sun  in  the  fol- 
lowing order,  and  complete  their  revolutions  in  the  follow- 
ing times,  computed  in  our  days  and  years.  Beginning 
with  that  nearest  to  the  sun,  Mercury  performs  his  revolu- 
tion in  87  days  and  23  hours  ;  Venus,  in  224  days,  17  hours ; 
the  Earth,  attended  by  the  moon,  in  365  days,  6  hours  j 
Mars,  in  one  year,  322  days ;  Ceres,  in  4  years,  7  months, 
and  10  days;  Pallas,  in  4  years,  7  months,  and  10  days; 
Juno,  in  4  years  and  128  days ;  Vesta,  in  3  years,  66  days, 
and  4  hours;  Jupiter,  in  11  years,  315  days,  and  15  hours; 
Saturn,  in  29  years,  161  days,  and  19  hours  ;  Herschel,  in 
83  years,  342  days,  and  4  hours. 

752.  A  year  consists  of  the  time  which  it  takes  a  planet 
to  perform  one  complete  revolution  through  its  orbit,  or  to 
pass  once  around  the  sun.     Our  earth  performs  this  revolu- 
tion in  365  days,  and  therefore  this  is  the  period  of  our  year. 
Mercury  completes  her  revolution  in  88  days,  and  therefore 
her  year  is  no  longer  than  88  of  our  days.     But  the  planet 
Herschel  is  situated  at  such  a  distance  from  the  sun,  that  his 
revolution  is  not  completed  in  less  than  about  84  of  our 
years.     The  other  planets  complete  their  revolutions  in  va- 
rious periods  of  time,  between  these ;  so  that  the  time  of 
these  periods  is  generally  in  proportion  to  the  distance  of 
each  planet  from  the  sun. 

Ceres,  Pallas,  Juno,  and  Vesta,  are  the  smallest  of  all  the 
planets,  and  are  called  Asteroids. 

Besides  the  above  enumerated  primary  planets,  our  sys- 
tem contains  eighteen  secondary  planets,  or  moons.  Of 
these,  our  Earth  has  one  moon,  Jupiter  four,  Saturn  seven, 
and  Herschel  six.  None  of  these  moons,  except  our  own, 
and  one  or  two  of  Saturn's,  can  bs  seen  without  a  telescope. 
The  seven  other  planets,  so  far  as  has  been  discovered,  are 
entirely  without  moons. 

753.  All  the  planets  move  around  the  sun  from  west  to 

What  are  those  called,  which  revolve  around  these  primaries  as  a 
centre  1  In  what  order  are  the  several  planets  situated,  in  respect  to  the 
sun  1  How  long  does  it  take  each  planet  to  make  its  revolution  around 
the  sun  1  What  is  a  year  1  What  planets  are  called  asteroids?  How 
many  moons  does  our  system  contain  1  Which  of  the  planets  are  at- 
tended by  moons,  and  how  many  has  each  1  In  what  direction  do  the 
planets  move  around  the  sun? 

30 


230  ASTRONOMY. 

east,  and  in  the  same  direction  do  the  moons  revolve  around 
their  primaries,  with  the  exception  of  those  of  Herschel, 
which  appear  to  revolve  in  a  contrary  direction. 

754.  The  paths  in  which  the  planets  move  round  the  sun, 
and  in  which  the  moons  move  round  their  primaries,  are 
called  their  orbits.     These  orbits  are  not  exactly  circular,  as 
they  are  commonly  represented  on  paper,  but  are  elliptical, 
or  oval,  so  that  all  the  planets  are  nearer  the  sun,  when  in 
one  part  of  their  orbits,  than  when  in  another. 

In  addition  to  their  annual  revolutions,  some  of  the  plan- 
ets are  known  to  have  diurnal,  or  daily  revolutions,  like  our 
earth.  The  periods  of  these  daily  revolutions  have  been 
ascertained,  in  several  of  the  planets,  by  spots  on  their  sur- 
faces. But  where  no  such  mark  is  discernible,  it  cannot  be 
ascertained  whether  the  planet  has  a  daily  revolution  or  not, 
though  this  has  been  found  to  be  the  case  in  every  instance 
where  spots  are  seen,  and,  therefore,  there  is  little  doubt  but 
all  have  a  daily,  as  well  as  a  yearly  motion. 

755.  The  axis  of  a  planet  is  an  imaginary  line  passing 
through  its  centre,  and  about  which  its  diurnal  revolution  is 
performed.     The  poles  of  the  planets  are  the  extremities  of 
this  axis. 

756.  The  orbits  of  Mercury  and  Venus  are  within  that 
of  the  earth,  and  consequently  they  are  called  inferior  plan- 
ets.    The  orbits  of  all  the  other  planets  are  without,  or  ex- 
terior to  that  of  the  earth,  and  these  are  called  superior 
planets. 

That  the  orbits  of  Mercury  and  Venus  are  within  that 
of  the  earth,  is  evident  from  the  circumstance,  that  they  are 
never  seen  in  opposition  to  the  sun,  that  is,  they  never  ap- 
pear in  the  west,  when  the  jsun  is  in  the  east.  On  the  con- 
trary, the  orbits  of  all  the  other  planets  are  proved  to  be  out- 
side of  the  earth's,  since  these  planets  are  sometimes  seen 
in  opposition  to  the  sun. 

This  will  be  understood  by  fig.  191,  where  suppose  s  to 
be  the  sun,  m  the  orbit  of  Mercury  or  Venus,  e  the  orbit  of 
the  earth,  and^'  that  of  Jupiter.  Now,  it  is  evident,  that  if 


What  is  the  orbit  of  a  planet  ?  What  revolutions  have  the  planets, 
besides  their  yearly  revolutions'?  Have  all  ,the  planets  diurnal  revo- 
lutions'? How  is  it  known  that  the  planets  have  daily  revolutions'? 
What  is  the  axis  of  a  planet  1  What  is  the  pole  of  a  planet  1  Which 
are  the  superior,  and  which  the  inferior  planets  1  How  is  it  proved 
that  the  inferior  planets  are  within  (he  earth's  orbit,  and  the  superior 
ones  without  it  1 


ASTRONOMY. 


231 


a  spectator  be  placed  any  Fig.  191. 

where  in  the  earth's  or- 
oit,  as  at  e,  he  may  some- 
times see  Jupiter  in  op- 
position to  the  sun,  as  at 
j,  because  then  the  spec- 
tator would  be  between 
Jupiter  and  the  sun.  But 
the  orbit  of  Venus,  being 
surrounded  by  that  of  the 
earth,  she  never  can  come 
in  opposition  to  the  sun, 
or  in  that  part  of  the 
heavens  opposite  to  him, 
as  seen  by  us,  because 
our  earth  never  passes  between  her  and  the  sun. 

757.  It  has  already  been  stated,  that  the  orbits  of  the 
planets  are  elliptical,  and  that,  consequently,  these  bodies 
are  sometimes  nearer  the  sun  than  at  others.     An  ellipse, 
or  oval,  has  two  foci,  and  the  sun,  instead  of  being  in  the 
common  centre,  is  always  in  the  lower  foci  of  their  orbits. 

The  orbit  of  a  planet 
is  represented  by  fig. 
192,  where  a,  d,  bt  e,  is 
an  ellipse,  with  its  two 
foci,  s  and  0,  the  sun  be- 
ing in  the  focus  s,  which 
is  called^the  lower  focus. 

When  the  earth,  or 
any  other  planet,  revolv- 
ing around  the  sun,  is  in 
that  part  of  its  orbit  near- 
est the  sun,  as  at  a,  it  is  said  to  be  in  its  perihelion ;  and  when 
in  that  part  which  is  at  the  greatest  distance  from  the  sun, 
as  at  b,  it  is  said  to  be  in  its  aphelion.  The  line  s,  d,  is  the 
mean,  or  average  distance  of  a  planet's  orbit  from  the  sun. 

758.  ECLIPTIC. — The  planes  of  the  orbits  of  all  the 
planets  pass  through  the  centre  of  the  sun.     The  plane  of 
an  orbit  is  an  imaginary  surface,  passing  from  one  extremity, 
or  side  of  the  orbit,  to  the  other.     If  the  rim  of  a  drum 


Explain  fig.  191,  and  show  why  the  inferior  planets  never  can  be  in 
opposition  to  the  sun.  What  are  the  shapes  of  the  planetary  orbits? 
What  is  meant  by  perihelion  1  What  is  the  plane  of  an  orbit  1 


232 


ASTRONOMY. 


head  be  considered  the  orbit,  its  plane  would  be  the  parch 
ment  extended  across  it,  on  which  the  drum  is  beaten. 

Let  us  suppose  the  earth's  orbit  to  be  such  a  plane,  cut- 
ting the  sun  through  his  centre,  and  extending  out  on  every 
side  to  the  starry  heavens ;  the  great  circle  so  made,  would 
mark  the  line  of  the  ecliptic,  or  the  sun's  apparent  path 
through  the  heavens. 

This  circle  is  called  the  sun's  apparent  path,  because  the 
revolution  of  the  earth  gives  the  sun  the  appearance  of  pass- 
ing through  it.  It  is  called  the  ecliptic,  because  eclipses 
happen  when  the  moon  is  in,  or  near,  this  apparent  path. 

759.  ZODIAC. — The   Zodiac   is   an  imaginary  belt,    or 
broad   circle,  extending  quite  around  the  heavens.     The 
ecliptic  divides  the  zodiac  into  two  equal  parts,  the  zodiac  ex- 
tending 8  degrees  on  each  side  of  the  ecliptic,  and  therefore 
is  16  degrees  wide.     The  zodiac  is  divided  into   12  equal 
parts,  called  the  signs  of  the  zodiac. 

760.  The  sun  appears  every  year  to  pass  around  the  grear 
circle  of  the  ecliptic,  and  consequently,  through  the  12  con- 
stellations, or  signs  of  the  zodiac.     But  it  will  be  seen,  IP 
another  place,  that  the  sun,  in  respect  to  the  earth,  stand? 
still,  and  that  his  apparent  yearly  course  through  the  heav 
ens  is  caused  by  the  annual  revolution  of  the  earth  around 
its  orbit.  Fig.  193. 

To  understand  the  cause  of  this 
deception,  let  us  suppose  that  s,  fig. 
193,  is  the  sun,  a  b,  a  part  of  the 
circle  of  the  ecliptic,  and  c  d,  a 
part  of  the  earth's  orbit.  Now,  if 
a  spectator  be  placed  at  c,  he  will 
see  the  sun  in  that  part  of  the  eclip- 
tic marked  by  b,  but  when  the  earth 
moves  in  her  annual  revolution  to 
d,  the  spectator  will  see  the  sun  in 
that  part  of  the  heavens  marked 
by  a;  so  that  the  motion  of  the 
earth  in  one  direction,  will  give  the 
sun  an  apparent  motion  in  the  con- 
trary direction. 

Explain  what  is  meant  by  the  ecliptic.  Why  is  the  ecliptic  called 
the  sun's  apparent  path  1  What  is  the  zodiac  1  How  does  the  ecliptic 
divide  the  zodiac?  How  far  does  the  zodiac  extend  on  each  side  of  the 
ecliptic  ?  Explain  fig.  193,  and  show  why  the  sun  seems  to  pass  through 
the  ecliptic,  when  the  earth  only  revolves  around  the  sun. 


ASTRONOMY.  233 

761.  A  sign,  or  constellation,  is  a  collection  of  fixed  stars, 
and,  as  \ve  have  already  seen,  the  sun  appears  to  move 
through  the  twelve  signs  of  the  zodiac  every  year.     Now, 
the  sun's  place  in  the  heavens,  or  zodiac,  is  found  by  his  ap- 
parent conjunction,  or  nearness  to  any  particular  star  in  the 
constellation.     Suppose  a  spectator  at  c,  observes  the  sun  to 
be  nearly  in  a  line  with  the  star  at  b,  then  the  sun  would 
be  near  a  particular  star  in  a  certain  constellation.     When 
the  earth  moves  to  d,  the  sun's  place  would  assume  another 
direction,  and  he  would  seem  to  have  moved  into  another 
constellation,  and  near  the  star  a. 

762.  Each  of  the  12  signs  of  the  zodiac  is  divided  into 
30  smaller  parts,  called  degrees ;  each  degree  into  60  equal 
parts,  called  minutes,  and  each  minute  into  60  parts,  called 
seconds. 

The  division  of  the  zodiac  into  signs,  is  of  very  ancient 
date,  each  sign  having  also  received  the  name  of  some  ani- 
mal, or  thing,  which  the  constellation,  forming  that  sign, 
was  supposed  to  resemble.  It  is  hardly  necessary  to  say, 
that  this  is  chiefly  the  result  of  imagination,  since  the  fig- 
ures made  by  the  places  of  the  stars,  never  mark  the  out- 
lines of  the  figures  of  animals,  or  other  things.  This  is, 
however,  found  to  be  the  most  convenient  method  of  finding 
any  particular  star  at  this  day,  for  among  astronomers,  any 
star,  in  each  constellation,  may  be  designated  by  describing 
the  part  of  the  animal  in  which  it  is  situated.  Thus,  by 
knowing  how  many  stars  belong  to  the  constellation  Leo, 
or  the  Lion,  we  readily  know  what  star  is  meant  by  that 
which  is  situated  on  the  Lion's  ear  or  tail. 

763.  The  names  of  the  12  signs  of  the  zodiac  are,  Aries, 
Taurus,  Gemini,  Cancer,  Leo,  Virgo,  Libra,  Scorpio,  Sa- 
gittarius, Capricorn,  Aquarius,  and  Pisces.     The  common 
names,  or  meaning  of  these  words,  in  the  same  order,  are, 
the  Ram,  the  Bull,  the  Twins,  the  Crab,  the  Lion,  the  Vir- 
gin, the  Scales,  the  Scorpion,  the  Archer,  the  Goat,  the 
Waterer,  and  the  Fishes. 


What  is  a  constellation,  or  sign"?  How  is  the  sun's  apparent  place 
in  the  heavens  found  1  Into  how  many  parts  are  the  signs  of  the  zo- 
diac divided,  and  what  are  these  parts  called  1  Is  there  any  resem- 
blance between  the  places  of  the  stars,  and  the  figures  of  the  animals 
after  which  they  are  called  1  Explain  why  this  is  a  convenient  method 
of  finding  any  particular  Ptar  in  a  sign  1  What  are  the  names  of  the 
twelve  si^ns^ 

20* 


234 


ASTRONOMY. 


The  twelve  signs  of  the  zodiac,  together  with  the  sun, 
and  the  earth  revolving  around  him,  are  represented  at  fig 
Fig.  194. 


194.  When  the  earth  is  at  A,  the  sun  will  appear  to  be  just 
entering  the  sign  Aries,  hecause  then,  when  seen  from  the 
earth,  he  ranges  towards  certain  stars  at  the  beginning  of 
that  constellation.  When  the  earth  is  at  C,  the  sun  will 
appear  in  the  opposite  part  of  the  heavens,  and  therefore  in 
the  beginning  of  Libra.  The  middle  line,  dividing  the  cir- 
cle of  the  zodiac  into  equal  parts,  is  the  line  of  the  ecliptic. 
764.  DENSITY  OF  THE  PLANETS.— Astronomers  have  no 
means  of  ascertaining  whether  the  planets  are  composed  of 
the  same  kind  of  matter  as  our  earth,  or  whether  their  sur- 
faces are  clothed  with  vegetables  and  forests,  or  not.  They 
have,  however,  been  able  to  ascertain  the  densities  of  se- 
veral of  them^  by  observations  on  their  mutual  attraction. 

Explain  why  the  sun  will  be  in  the  beginning  of  Aries,  when  the 
earth  is  at  A.  fig.  191*  How  has  the  density  of  the  planets  been  as- 
certained 1 


ASTRONOMY.  235 

By  density,  is  meant  compactness,  or  the  quantity  of  matter 
in  a  given  space.  When  two  bodies  are  of  equal  bulk,  that 
which  weighs  most,  has  the  greatest  density.  It  was  shown, 
while  treating  of  the  properties  of  bodies,  that  substances 
attract  each  other  in  proportion  to  the  quantities  of  matter 
they  contain.  If,  therefore,  we  know  the  dimensions  of 
several  bodies,  and  can  ascertain  the  proportion  in  which 
they  attract  each  other,  their  quantities  of  matter,  or  densi- 
ties, are  easily  found. 

765.  Thus,  when  the  planets  pass  each  other  in  their 
circuits  through  the  heavens,  they  are  often  drawn  a  little 
out  of  the  lines  of  their  orbits  by  mutual   attraction.     As 
bodies  attract  in  proportion  to  their  quantities  of  matter,  it 
is  obvious  that  the  small  planets,  if  of  the  same  density, 
will  suffer  greater  disturbance  from  this  cause,  than  the 
large  ones.     But  suppose  two  planets,  of  the  same  dimen- 
sions, pass  each  other,  and  it  is  found  that  one  of  them  is 
attracted  twice  as  far  out  of  its  orbit  as  the  other,  then,  by 
the  known  laws  of  gravity,  it  would  be  inferred,  that  one  of 
them  contained  twice  the  quantity  of  matter  that  the  other 
did,  and  therefore  that  the  density  of  the  one  was  twice  that 
of  the  other. 

By  calculations  of  this  kind,  it  has  been  found,  that  the 
density  of  the  sun  is  but  a  little  greater  than  that  of  water, 
while  Mercury  is  more  than  nine  times  as  dense  as  water, 
having  a  specific  gravity  nearly  equal  to  that  of  lead.  The 
earth  has  a  density  about  five  times  greater  than  that  of  the 
sun,  and  a  little  less  than  half  that  of  Mercury.  The  densi- 
ties of  the  other  planets  seem  to  diminish  in  proportion  as 
their  distances  from  the  sun  increase,  the  density  of  Saturn, 
one  of  the  most  remote  of  planets,  being  only  about  one 
third  that  of  water. 

THE  SUN. 

766.  The  sun  is  the  centre  of  the  solar  system,  and  the 
great  dispenser  of  heat  and  light  to  all  the  planets.    Around 
the  sun  all  the  planets  revolve,  as  around  a  common  centre, 
he  being  the  largest  body  in  our  system,  and,  so  far  as  we 
know,  the  largest  in  the  universe. 

What  is  meant  by  density  ?  In  what  proportion  do  bodies  attract 
each  other?  How  are  the  deputies  of  the  planets  ascertained  1  What 
is  the  density  of  the  sun,  of  Mercury,  and  of  the  earth  1  In  what  pro- 
portions do  the  densities  of  the  planets  appear  to  diminish  1  Where  is 
the  place  of  the  sun,  in  the  solar  system  1 


236  ASTRONOMY. 

767.  The  distance  of  the  sun  from  the  earth  is  95  mil- 
lions of  miles,  and  his  diameter  is  estimated  at  88,000  miles. 
Our  globe,  when  compared  with  the  magnitude  of  the  sun, 
is  a  mere  point,  for  his  bulk   is  about  thirteen  hundred 
thousand  times  greater  than  that  of  the  earth.     Were  the 
sun's  centre  placed  in  the  centre  of  the  moon's  orbit,  his 
circumference  would   reach   two  hundred  thousand  miles 
beyond  her  orbit  in  every  direction,  thus  filling  the  whole 
space  between  us  and  the  rnoon,  and  extending  nearly  as  far 
beyond  her  as  she  is  from  us.     A  traveller,  who  should  go 
at  the  rate  of  90  miles  a  day,  would  perform  a  journey  of 
nearly  33,000  miles  in  a  year,  and  yet  it  would  take  such  a 
traveller  more  than  80  years  to  go  round  the  circumference 
of  the  sun.     A  body  of  such  mighty  dimensions,  hanging 
on  nothing,  it  is  certain,  must  have  emanated  from  an  Al- 
mighty power. 

768.  The  sun  appears  to  move  around  the  earth  every  24 
hours,  rising  in  the  east,  and  setting  in  the  west.     This  mo- 
tion, as  \vill  be  proved  in  another  place,  is  only  apparent, 
and  arises  from  the  diurnal  revolution  of  the  earth. 

769.  The  sun,  although  he  does  not,  like  the  planets,  re- 
volve in  an  orbit,  is,  however,  not  without  motion,  having  a 
revolution  around  his  own  axis,  once  in  25  days  and  10 
hours.     Both  the  fact  that  he  has  such  a  motion,  and  the 
time  in  which  it  is  performed,  have  been  ascertained  by  the 
spots  on  his  surface.     If  a  spot  is  seen,  on  a  revolving  body, 
in  a  certain  direction',  it  is  obvious,  that  when  the  same  spot 
is  again  seen,  in  the  same  direction,  that  the  body  has  made 
one  revolution.     By  such  spots  the  diurnal  revolutions  of 
the  planets,  as  well  as  the  sun,  have  been  determined. 

770.  Spots  on  the  sun  seem  first  to  have  been  observed  in 
the  year  1611,  since  which  time  they  have  constantly  at 
tracted  attention,  and  have  been  the  subject  of  investigation 
among  astronomers.      These  spots   change   their   appear- 
ance as  the  sun  revolves  on  his  axis,  and  become  greater  or 
less,  to  an  observer  on  the  earth,  as  they  are  turned  to,  or 
from  him  ;  they  also  change  in  respect  to  real   magnitude 
and  number  :  one  spot,  seen  by  Dr.  Herschel,  was  estimated 

What  is  the  distance  of  the  sun  frorn  the,  earth  1  What  is  the  di- 
ameter of  the  sun  "?  Suppose  the  centre  of  the  sun  and  that  of  the 
moon's  orbit  to  be  coincident,  how  far  would  the  sun  extend  beyond 
the  moon's  orbit  1  How  is  it  proved  that  the  sun  has  a  motion  around 
nis  own  axis!  How  often  does  the  sun  revolve]  When  were  spots 
of  the  sun  first  observed  1 


ASTRONOMY.  237 

to  be  more  than  six  times  the  size  of  our  earth,  being  50,000 
miles  in  diameter.  Sometimes  forty  or  fifty  spots  may  he 
seen  at  the  same  time,  and  sometimes  only  one.  They  are 
often  so  large  as  to  be  seen  with  the  naked  eye ;  this  was  the 
case  in  1816. 

771.  In  respect  to  the  nature  and  design  of  these  spots, 
almost    every  astronomer   has   formed  a  different   theory. 
Some  have  supposed  them  to  be  solid  opaque  masses  of 
scoriae,  floating  in  the  liquid   fire  of  the   sun ;    others,   as 
satellites,  revolving  round  him,  and  hiding  his  light  from 
us;  others,  as  immense  masses,  which  have  fallen  on  his 
disc,  and  which  are  dark  coloured,  because  they  have  not 
yet  become  sufficiently  heated.     In   two   instances,  these 
spots  have  been  seen  to  burst  into  several  parts,  and  the  parts 
to  fly  in  several  directions,  like  a  piece  of  ice  thrown  upon 
the  ground.     Others  have  supposed  that  these  dark  spots 
were  the  body  of  the  sun,  which  became  visible  in  conse- 
quence of  openings  through  the  fiery  matter,  with  which  he 
is  surrounded.     Dr.  Herschel,  from  many  observations  with 
his  great  telescope,  concludes,  that  the  shining  matter  of  the 
sun  consists  of  a  mass  of  phosphoric  clouds,  and  that  the 
spots  on  his  surface  are  owing  to  disturbances  in  the  equili- 
brium of  this  luminous  matter,  by  which  openings  are  made 
through  it.     There  are,  however,  objections  to  this  theory, 
as  indeed  there  are  to  all  the  others,  and  at  present  it  can 
only  be  said,  that  no  satisfactory  explanation  of  the  cause  of 
these  spots  has  been  given. 

772.  That  the  sun,  at  the  same  time  that  he  is  the  great 
source  of  heat  and  light  to  all  the  solar  worlds,  may  yet  be 
capable  of  supporting  animal  life,  has  been  the  favourite 
doctrine  of  several  able  astronomers.     Dr.  Wilson  first  sug- 
gested that  this  might  be  the  case,  and  Dr.  Herschel,  with 
his  telescope,  made  observations  which  confirmed  him  in 
this  opinion.     The  latter  astronomer  supposed  that  the  func- 
tions of  the  sun,  as  the  dispenser  of  light  and  heat,  might 
be  performed  by  a  luminous,  or  phosphoric  atmosphere,  sur- 
rounding him  at  many  hundred  miles  distance,  while  his 
solid  nucleus  might  be  fitted  for  the  habitations  of  millions 
of  reasonable  beings.     This  doctrine  is,  however,  rejected 
by  most  writers  on  the  subject  at  the  present  day. 

What  has  been  the  difference  in  the  number  of  spots  observed  7 
What  was  the  size  of  the  spot  seen  by  Dr.  Herschel  1  What  has  been 
advanced  concerning  the  nature  of  these  spots  1  Have  they  been  ac- 
counted for  satisfactorily "?  What  is  said  concerning  the  sun  s  being  a 
habitable  globe? 


ASTRONOMY. 

MERCURY. 

773.  Mercury,  the  planet  nearest  the  sun,  is  about  3000 
miles  in  diameter,  and  revolves  around  him,  at  the  distance 
of  37  millions  of  miles.     The  period  of  his  annual  revolu- 
tion is  87  days,  and  he  turns  on  his  axis  once  in   about  24 
hours. 

The  nearness  of  this  planet  to  the  sun,  and  the  short  time 
his  fully  illuminated  disc  is  turned  towards  the  earth,  has 
prevented  astronomers  from  making  many  observations  on 
him. 

No  signs  of  an  atmosphere  have  been  observed  in  this 
planet.  The  sun's  heat  at  Mercury  is  about  seven  times 
greater  than  it  is  on  the  earth,  so  that  water,  if  nature  fol- 
lows the  same  laws  there  that  she  does  here,  cannot  exist  at 
Mercury,  except  in  the  state  of  steam. 

The  nearness  of  this  planet  to  the  sun,  prevents  his  being 
often  seen.  He  may,  however,  sometimes  be  observed  just 
before  the  rising,  and  a  little  after  the  setting  of  the  sun. 
When  seen  after  sunset,  he  appears  a  brilliant,  twinkling 
star,  showing  a  white  light,  which,  however,  is  much  ob- 
scured by  the  glare  of  twilight.  When  seen  in  the  morn- 
ing, before  the  rising  of  the  sun,  his  light  is  also  obscured 
by  the  sun's  rays. 

Mercury  sometimes  crosses  the  disc  of  the  sun,  or  comes 
between  the  earth  and  that  luminary,  so  as  to  appear  like  a 
small  dark  spot  passing  over  the  sun's  face.  This  is  called 
the  transit  of  Mercury. 

VENUS. 

774.  Venus  is  the  other  planet,  whose  orbit  is  within  that 
of  the  earth.     Her   diameter  is   about  8600  miles,  being 
somewhat  larger  than  the  earth. 

Her  revolution  around  the  sun  is  performed  in  224  days, 
at  the  distance  of  68  millions  of  miles  from  him.  She  turns 
on  her  axis  once  in  23  hours,  so  that  her  day  is  a  little 
shorter  than  ours. 

775.  Venus,  as  seen  from  the  earth,  is  the  most  brilliant 
of  all  the  primary  planets,  and  is  better  known  than  any 

What  is  the  diameter  of  Mercury,  and  what  are  his  periods  of 
annual  and  diurnal  revolution  1  How  great  is  the  sun's  heat  at  Me *•- 
cury  1  At  what  times  is  Mercury  to  be  seen  1  What  is  a  transit  of 
Mercury  1  Where  is  the  orbit  of  Venus,  in  respect  to  that  of  the 
earth  1  What  is  the  time  of  Venus'  revolution  round  the  sun  1  How 
often  does  she  turn  on  her  axis  1 


ASTRONOMY.  239 

nocturnal  luminary  except  the  moon.  When  seen  through 
a  telescope,  she  exhibits  the  phases  or  horned  appearance 
of  the  moon,  and  her  face  is  sometimes  variegated  with  dark 
spots.  Venus  may  often  be  seen  in  the  day  time,  even  when 
she  is  in  the  vicinity  of  the  blazing  light  of  the  sun.  A 
luminous  appearance  around  this  planet,  seen  at  certain 
times,  proves  that  she  has  an  atmosphere.  Some  of  her 
mountains  are  several  times  more  elevated  than  any  on  our 
globe,  being  from  10  to  22  miles  high.  Venus  sometimes 
makes  a  transit  across  the  sun's  disc,  in  the  same  manner 
as  Mercury,  already  described.  The  transits  of  Venus  oc- 
cur only  at  distant  periods  from  each  other.  The  last  transit 
was  in  1769,  and  the  next  will  not  happen  until  1874. 
These  transits  have  been  observed  by  astronomers  with  the 
greatest  care  and  accuracy,  since  it  is  by  observations  on 
them  that  the  true  distances  of  the  earth  and  planets  from 
the  sun  are  determined. 

776.  When  Venus  is  in  that  part  of  her  orbit  which  gives 
her  the  appearance  of  being  west  of  the  sun,  she  rises  before 
him,  and  is  then  called  the  morning  star ;  and  when  she 
appears  east  of  the  sun,  she  is  behind  him  in  her  course,  and 
is  then  called  the  evening  star.     These  periods  do  not  agree, 
either  with  the  yearly  revolution  of  the  earth,  or  of  Venus, 
for  she  is  alternately  290  days  the  morning  star,  and  290 
days  the  evening  star.     The  reason  of  this  is,  that  the  earth 
and  Venus  move  round  the  sun  in  the  same  direction,  and 
hence  her  relative  motion,  in  respect  to  the  earth,  is  much 
slower  than  her  absolute  motion  in  her  orbit.     If  the  earth 
had  no  yearly  motion,  Venus  would  be  the  morning  star 
one  half  of  the  year,  and  the  evening  star  the  other  half. 

THE  EARTH. 

777.  The  next  planet  in  our  system,  nearest  the  sun,  is 
the  Earth.     Her  diameter  is  7912  miles.     This  planet  re- 
volves around  him  in  365  days,  5  hours,  and  48  minutes; 
and  at  the  distance  of  95  millions  of  miles.     It  turns  round 
its  own  axis  once  in  24  hours,  making  a  day  and  a  night. 
The  Earth's  revolution  around  the  sun  is  called  its  annual, 
or  yearly  motion,  because  it  is  performed  in  a  year ;  while 

What  is  said  of  the  height  of  the  mountains  in  Venus?  On  what 
account  are  the  transits  of  Venus  observed  with  great  care  1  When  is 
Venus  the  morning,  and  wh^n  the  evening  star7?  How  long  is  Venus 
the  morning,  and  how  long  the  evening  star  ]  How  long  does  it  take  the 
earth  to  revolve  round  the.  sun  1 


240  ASTRONOMY. 

the  revolution  around  its  own  axis,  is  called  the  diurnal  01 
daily  motion,  because  it  takes  place  every  day.  The  figurt 
of  the  earth,  with  the  phenomena  connected  with,  her  motion, 
will  be  explained  in  another  place. 

THE  MOON. 

778.  The  Moon,  next  to  the  sun,  is,  to  us,  the  most  bril- 
liant and  interesting  of  all  the  celestial  bodies.     Being  the 
nearest  to  us  of  any  of  the  heavenly  orbs,  and  apparently 
designed  for  our  use,  she  has  been  observed  with  great  at- 
tention, and  many  of  the  phenomena  which  she  presents, 
are  therefore  better  understood  and  explained,  than  those  of 
the  other  planets. 

While  the  earth  revolves  round  the  sun  in  a  year,  it  is 
attended  by  the  Moon,  which  makes  a  revolution  round  the 
earth  once  in  27  days,  7  hours,  and  43  minutes.  The  dis- 
tance of  the  Moon  from  the  earth  is  240,000  miles,  and  her 
diameter  about  2000  miles. 

Her  surface,  when  seen  through  a  telescope,  appears 
diversified  with  hills,  mountains,  valleys,  rocks,  and  plains, 
presenting  a  most  interesting  and  curious  aspect :  but  the 
explanation  of  these  phenomena  are  reserved  for  another 
section. 

MARS. 

779.  The  next  planet  in  the  solar  system,  is  Mars,  his 
orbit  surrounding  that  of  the  earth.     The  diameter  of  this 
planet  is  upwards  of  4000  miles,  being  about  half  that  of 
the  earth.     The  revolution  of  Mars  around  the  sun  is  per- 
formed in  nearly  687  days,  or  in  somewhat  less  than  two  of 
our  years,  and  he  turns  on  his  axis  once  in  24  hours  and  40 
minutes.     His  mean  distance  from  the  sun  is  144  millions 
of  miles,  so  that  he  moves  in  his  orbit  at  the  rate  of  about 
55,000  miles  in  an  hour.     The  days  and  nights,  at  this 
planet,  and  the  different  seasons  of  the  year,  bear  a  consider- 
able resemblance  to  those  of  the  earth.     The  density  of 
Mars  is  less  than  that  of  the  earth,  being  only  three  times 
that  of  water. 


What  is  meant  by  the  earth's  annual  revolution,  and  what  by  her 
diurnal  revolution  1  Why  are  the  phenomena  of  the  moon  better  ex- 
plained than  those  of  the  other  planets  7  In  what  time  is  a  revolution 
of  the  moon  about  the  earth  performed  ?  What  is  the  distance  of  the 
moon  from  the  earth  1  What  is  the  diameter  of  Mars  1  How  much 
longer  is  a  year  at  Mars  than  our  yenr  1  What  is  his  rate  of  motion 
in  his  orbit  1 


ASTRONOMY.  241 

Mars  reflects  a  dull  red  light,  by  which  he  may  be  dis- 
tinguished from  the  other  planets.  His  appearance  through 
the  telescope  is  remarkable  for  the  great  number  and  variety 
of  spots  which  his  surface  presents. 

Mars  has  an  atmosphere  of  great  density  and  extent,  as 
is  proved  by  the  dim  appearance  of  the  fixed  stars,  when 
seen  through  it.  When  any  of  the  stars  are  seen  nearly  in 
a  line  with  this  planet,  they  give  a  faint,  obscure  light,  and 
the  nearer  they  approach  the  line  of  his  disc,  the  fainter  is 
their  light,  until  the  star  is  entirely  obscured  from  the  sight. 

This  planet  sometimes  appears  much  larger  to  us  than  at 
others,  and  this  is  readily  accounted  for  by  his  greater  or 
less  distance.  At  his  nearest  approach  to  the  earth,  hir, 
distance  is  only  50  millions  of  miles,  while  his  greatest  dis 
tance  is  240  millions  of  miles ;  making  a  difference  in  his 
distance  of  190  millions  of  miles,  or  the  diameter  of  the 
earth's  orbit. 

The  sun's  heat  at  this  planet  is  less  than  half  that  which 
we  enjoy. 

To  the  inhabitants  of  Mars,  our  planet  appears  alternately 
as  the  morning  and  evening  star,  as  Venus  does  to  us. 
VESTA,  JUNO,  PALLAS,  AND  CERES 

780.  These  planets  were  unknown  until  recently,  and 
are  therefore  sometimes  called  the  new  planets.     It  has  been 
mentioned,  that  they  are  also  called  Asteroids. 

78 1.  The  orbit  of  Vesta  is  next  in  the  solar  system  to  that 
of  Mars.     This  planet  was  discovered  by  Dr.  Olbers,  of 
Bremen,  in  1807.     The  light  of  Vesta  is  of  a  pure  white, 
and  in  a  clear  night  she  may  be  seen  with  the  naked  eye, 
appearing  about  the  size  of  a  star  of  the  5th  or  6th  magni- 
tude.    Her  revolution  round  the  sun  is  performed  in  3  years 
and  66  days,  at  the  distance  of  223  millions  of  miles  from 
him. 

782.  Juno  was  discovered  by  Mr.  Harding,  of  Bremen, 
in  1804.     Her  mean  distance  from  the  sun  is  253  millions 
of  miles.     Her  orbit  is  more  elliptical  than  that  of  any  other 
planet,  and,  in  consequence,  she  is  sometimes  127  millions 
of  miles  nearer  the  sun  than  at  others.     This  planet  com- 

What  is  his  appearance  through  the  telescope  1  How  is  it  proved 
that  Mars  has  an  atmosphere  of  great  density  1  Why  does  Mara 
sometimes  appear  to  us  larger  than  at  others  7  How  great  is  the  sun's 
heat  at  Mars  1  Which  are  the  new  planets,  or  asteroids  ?  When  was 
Vesta  discovered  1  What  is  the  period  of  Vesta's  annual,  revolution  1 
When  was  Juno  discovered  1  What  is  her  distance  from  the  sunl 
21 


242  ASTRONOMY. 

pletes  its  annual  revolution  in  4  years  and  about  4  months, 
and  revolves  round  its  axis  in  27  hours.  Its  diameter  is 
1400  miles. 

783.  Pallas  was  also  discovered  by  Dr.  Olbers,  in  1802. 
Its  distance  from  the  sun  is  226  millions  of  miles,  and  its 
periodic  revolution  round  him,  is  performed  in  4  years  and 
7  months. 

784.  Ceres  was  discovered  in  1801,  by  Piazzi,  of  Paler- 
mo.    This  planet  performs  her  revolution  in  the  same  time 
as  Pallas,  being  4  years  and  7  months.     Her  distance  from 
the  sun  260  millions  of  miles.     According  to  Dr.  Herschel, 
this  planet  is  ^nly  about  160  miles  in  diameter. 

JUPITER. 

785.  Jupiter  is  89,000  miles  in  diameter,  and  performs 
his  annual  revolution  once  in  about  1 1  years,  at  the  distance 
of  490  millions  of  miles  from  the  sun.     This  is  the  largest 
planet  in  the  solar  system,  being  about   1400  times  larger 
than  the  earth.     His  diurnal  revolution   is   performed  in 
nine  hours  and  fifty-five  minutes,  giving  his  surface,  at  the 
equator,  a  motion  of  28,000  miles  per  hour.     This  motion 
is  about  twenty  times  more  rapid  than  that  of  our  earth  at 
the  equator. 

786.  Jupiter,  next  to  Venus,  is  the  most  brilliant  of  the 
planets,  though  the  light  and  heat  of  the  sun  on  him  is  near- 
ly 25  times  less  than  on  the  earth. 

This  planet  is  distinguished  from  all  the  others,  by  an  ap- 
pearance resembling  bands,  which  extend  across  his  disc 
Fig.  175. 


What  is  the  period  of  her  revolution,  and  what  her  diameter  1 
What  is  said  of  Pallas  and  Ceres  1  What  is  the  diameter  of  Jupiter  1 
What  is  his  distance  from  the  sun!  What  is  the  period  of  Jupiter's 
diurnal  revolution  ?  What  is  the  sun's  heat  and  light  at  Jupiter,  when 
compared  with  that  of  the  earth  1  For  what  is  Jupiter  particularly  dis- 
tinguished? 


ASTRONOMY.  243 

These  are  termed  belts,  and  are  variable,  both  in  respect  to 
number  and  appearance.  Sometimes  seven  or  eight  are  seen, 
several  of  which  extend  quite  across  his  face,  while  others 
appear  broken,  or  interrupted. 

These  bands,  or  belts,  when  the  planet  is  observed  through 
a  telescope,  appear  as  represented  in  fig.  195.  This  ap- 
pearance is  much  the  most  common,  the  belts  running  quite 
across  the  face  of  the  planet  in  parallel  lines.  Sometimes, 
however,  his  aspect  is  quite  different  from  this,  for  in  1780, 
Dr.  Herschel  saw  the  whole  disc  of  Jupiter  covered  with 
small  curved  lines,  each  of  which  appeared  broken,  or  in- 
terrupted, the  whole  having  a  parallel  direction  across  his 
disc,  as  in  fig.  196. 

Fig.  196. 


Different  opinions  have  been  advanced  by  astronomers  re- 
specting the  cause  of  these  appearances.  By  some  they  have 
been  regarded  as  clouds,  or  as  openings  in  the  atmosphere 
of  the  planet,  while  others  imagine  that  they  are  the  marks 
of  great  natural  changes,  or  revolutions,  which  are  perpet- 
ually agitating  the  surface  of  that  planet.  It  is,  however, 
most  probable,  that  these  appearances  are  produced  by  the 
agency  of  some  cause,  of  which  we,  on  this  little  earth, 
must  always  be  entirely  ignorant. 

787.  Jupiter  has  four  satellites,  or  moons,  two  of  which 
are  sometimes  seen  with  the  naked  eye.  They  move  round, 
and  attend  him  in  his  yearly  revolution,  as  the  moon  does 
our  earth.  They  complete  their  revolutions  at  different  pe- 
riods, the  shortest  of  which  is  less  than  two  days,  and  the 
longest  seventeen  days. 

Is  the  appearance  of  Jupiter's  belts  always  the  same,  or  do  they 
change?  What  is  said  of  the  cause  of  Jupiter's  belted  appearance? 
How  many  moons  has  Jupiter,  and  what  are  the  periods  of  their  rev- 
olutions 1 


244  ASTRONOMY. 

These  satellites  often  fall  into  the  shadow  of  their  pri- 
mary, in  consequence  of  which  they  are  eclipsed,  as  seen 
from  the  earth.  The  eclipses  of  Jupiter's  moons  have  been 
observed  with  great  care  by  astronomers,  because  they  have 
been  the  means  of  determining  the  exact  longitude  of  places, 
and  the  velocity  with  which  light  moves  through  space. 
How  longitude  is  determined  by  these  eclipses,  cannot  be 
explained  or  understood  at  this  place,  hut  the  method  by 
which  they  become  the  means  of  ascertaining  the  velocity 
of  light,  may  be  readily  comprehended.  An  eclipse  of  one 
of  these  satellites  appears,  by  calculation,  to  take  place  six- 
teen minutes  sooner,  when  the  earth  is  in  that  part  of  hei 
orbit  nearest  to  Jupiter,  than  it  does  when  the  earth  is  in 
that  part  of  her  orbit  at  the  greatest  distance  from  him. 
Hence,  light  is  found  to  be  sixteen  minutes  in  crossing  the 
earth's  orbit,  and  as  the  sun  is  in  the  centre  of  this  orbit,  01 
nearly  so,  it  must  take  about  8  minutes  for  the  light  to  come 
from  him  to  us.  Light,  therefore,  passes  at  the  velocity  of 
95  millions  of  miles,  our  distance  from  the  sun,  in  about  8 
minutes,  which  is  nearly  200  thousand  miles  in  a  second. 

SATURN. 

788.  The  planet  Saturn  revolves  round  the  sun  in  a  pe- 
riod of  about  30  of  our  years,  and  at  the  distance  from  hiir» 
of  900  millions  of  miles.  His  diameter  is  79,000  miles, 
making  his  bulk  nearly  nine  hundred  times  greater  than 
that  of  the  earth,  but  notxvith standing  this  vast  size,  he  re- 
volves on  his  axis  once  in  about  ten  hours.  Saturn,  there- 
fore, performs  upwards  of  25,000  diurnal  revolutions  in  one> 
of  his  years,  and  hence  his  year  consists  of  more  than  25,006 
days;  a  period  of  time  equal  to  more  than  10,000  of  our 
days.  On  account  of  the  remote  distance  of  Saturn  from 
the  sun,  he  receives  only  about  a  90th  part  of  the  heat  and 
light  which  we  enjoy  on  the  earth.  But  to  compensate,  in 
some  degree,  for  this  vast  distance  from  the  sun,  Saturn  has 
seven  moons,  which  revolve  round  him  at  different  distances, 
and  at  various  periods,  from  1  to  80  days. 

What  occasions  the  eclipses  of  Jupiter's  moons  1  Of  what  use  are 
these  eclipses  to  astronomers  7  How  is  the  velocity  of  light  ascertain- 
ed by  the  eclipses  of  Jupiter's  satellites  1  What  is  the  time  of  Saturn's 
periodic  revolution  round  the  sun  1  What  is  his  distance  from  the  sun  1 
What  his  diameter"?  What  is  the  period  of  his  diurnal  revolution? 
How  many  days  make  a  year  at  Saturn  ?  How  many  moons  has 
Saturn  1 


ASTRONOMY.  245 

789.  Saturn  is  distinguished  from  the  other  planets  by  his 
ring,  as  Jupiter  is  by  his  belt.    When  this  planet  is  viewed 
through  a  telescope,  he  appears  surrounded  by  an  immense 
luminous  circle,  which  is  represented  by  fig.  197. 

There  are  indeed  two  luminous  circles,  or  rings,  one 
within  the  other,  with  a  dark  space  between  them,  so  that 
they  do  not  appear  to  touch  each  other.  Neither  does  the 

inner  ring  touch Fig.  197. 

the  body  of  the 
planet,  there  be- 
ing, by  estima- 
tion, about  the 
distance  of  thirty 
thousand  miles 
between  them. 
The  external 
circumference  of  the  outer  ring  is  640,000  miles,  and  its 
breadth  from  the  outer  to  the  inner  circumference,  7,200 
miles,  or  nearly  the  diameter  of  our  earth.  The  dark  space, 
between  the  two  rings,  or  the  interval  between  the  inner  and 
the  outer  ring,  is  2,800  miles. 

This  immense  appendage  revolves  round  the  sun  with 
the  planet,— performs  daily  revolutions  with  it,  and,  accord- 
ing to  Dr.  Herschel,  is  a  solid  substance,  equal  in  density 
to  the  body  of  the  planet  itself. 

790.  The  design  of  Saturn's  ring,  an  appendage  so  vast, 
and  so  different  from  any  thing  presented  by  the  other  plan- 
ets, has  always  been  a  matter  of  speculation  and  inquiry 
among  astronomers.     One  of  its  most  obvious  uses  appears 
to  be  that  of  reflecting  the  light  of  the  sun  on  the  body  of 
the  planet,  and  possibly  it  may  reflect  the  heat  also,  so  as  in 
some  degree  to  soften  the  rigour  of  so  inhospitable  a  climate. 

791.  As  this  planet  revolves  around  the  sun,  one  of  its 
sides  is  illuminated  during  one  half  of  the  year,  and  the 
other  side  during  the  other  half;  so  that,  as  Saturn's  year  is 
equal  to  thirty  of  our  years,  one  of  his  sides  will  be  en- 
lightened and  darkened,  alternately,  every  fifteen  years,  as 
the  poles  of  our  earth  are  alternately  in  the  light  and  dark 
every  year. 

Fig.  198  represents  Saturn  as  seen  by  an  eye,  placed  at 

How  is  Saturn  particularly  distinguished  from  all  the  other  planets  ? 
What  distance  is  there  between  the  body  of  Saturn  and  his  inner  ring? 
What  distance  is  there  between  his  inner  and  outer  ring  1  What  is 
the  circumference  of  the  outer  ring  7  How  long  is  one  of  Saturn's  sides 
alternately  in  the  light  and  dark? 

21* 


ASTRONOMY. 

right  angles  to  the  plane  of  his  ring.     When  seen  from  the 
earth,  his  position  is  al-  Fig.  198. 

ways  oblique,   as   repre-j 
sented  by  fig.  198. 

The  inner  white  circle,! 
represents  the  body  of  the 
planet,  enlightened  by  the 
sun.  The  dark  circle  next! 
to  this,  is  the  unenlighten- 
ed space  between  the  body  I 
of  the  planet  and  the  in- 
ner ring,  being  the  dark 
expanse  of  the   heavens 
beyond  the  planet.     The 
two  white  circles  are  the 
rings  of  the  planet,  with 
the   dark  space  between' 
them,  which  also  is  the  dark  expanse  of  the  heavens. 

HERSCHEL. 

792.  In  consequence  of  some  inequalities  in  the  motions 
of  Jupiter  and  Saturn,  in  their  orbits,  several  astronomers 
had  suspected  that  there  existed  another  planet  beyond  the 
orbit  of  Saturn,  by  whose  attractive  influence  these  irregu- 
larities were  produced.     The  conjecture  was  confirmed  by 
Dr.  Herschel,  in   1781,  who  in  that  year  discovered  the 
planet,  which  is  now  generally  known  by  the  name  of  its 
discoverer,  though  called  by  him  Georgium  sidus.     The 
orbit  of  Herschel  is  beyond  that  of  Saturn,  and  at  the  dis- 
tance of    1800  millions  of  miles  from  the  sun.     To  the 
naked  eye  this  planet  appears  like  a  star  of  the  sixth  mag- 
nitude, being,  with  the  exception  of  some  of  the  comets, 
the  most  remote  body,  so  far  as  is  known,  in  the  solar  system. 

793.  Herschel  completes  his  revolution  round  the  sun  in 
nearly  84  of  our  years,  moving  in  his  orbit  at  the  rate  of 
15,000  miles  in  an  hour.     His  diameter  is  35,000  miles: 
so  that  his  bulk  is  about  eighty  times  that  of  the  earth.    The 
light  and  heat  of  the  sun  at  Herschel,  is  about  360  times 
less  than  it  is  at  the  earth,  and  yet  it  has  been  found,  by  cal- 

In  what  position  is  Saturn  represented  by  fig.  198 1  What  circum- 
stance led  to  the  discovery  of  Herschel  1  In  what  year,  and  by  whom, 
was  Herschel  discovered  1  What  is  the  distance  of  Herschel  from  the 
sun?  In  what  period  is  his  revolution  round  the  sun  performed  1 
What  is  the  diameter  of  Herschel  ?  What  is  the  quantity  of  light  and 
heat  at  Herschel,  when  compared  with  that  of  the  earth  ? 


ASTRONOMY. 


24T 


eulation,  that  this  light  is  equal  to  248  of  our  full  moons,  a 
striking  proof  of  the  inconceivable  quantity  of  light  emitted 
by  the  sun. 

This  planet  has  six  satellites,  which  revolve  round  him 
at  various  distances,  and  in  different  times.  The  period  of 
some  of  these  have  been  ascertained,  while  those  of  the 
others  remain  unknown. 

Fig.  199. 


HerscfKl 


794.  Relative  situations  of  the  Planets. — Having  now 
given  a  short  account  of  each  planet  composing  the  solar 
system,  the  relative  situation  of  their  several  orbits,  with  the 
exception  of  those  of  the  Asteroids,  are  shown  by  fig.  199. 

In  the  figure,  the  orbits  are  marked  by  the  signs  of  each 
planet,  of  which  the  first,  or  that  nearest  the  sun,  is  Mer- 
cury, the  next  Venus,  the  third  the  Earth,  the  fourth  Mars; 
then  come  those  of  the  Asteroids,  then  Jupiter,  then  Saturn, 
and  lastly  Herschel. 


248  ASTRONOMY. 

795.  Comparative  dimensions  of  the  Planets. — The  com- 
parative dimensions  of  the  planets  are  delineated  at  fig.  200. 

Fiff.  200. 


MOTIONS  OF  THE  PLANETS. 

796.  It  is  said,  that  when  Sir  Isaac  Newton  was  near  de- 
monstrating the  great  truth,  that  gravity  is  the  cause  which 
keeps  the  heavenly  bodies  in  their  orbits,  he  became  so  agi- 
tated with  the  thoughts  of  the  magnitude  and  consequences 
of  his  discovery,  as  to  be  unable  to  proceed  with  his  demon- 
strations, and  desired  his  friend  to  finish  what  the  intensity 
of  his  feelings  would  not  allow  him  to  complete. 

We  have  seen,  in  a  former  part  of  this  work,  that  all  un- 
disturbed motion  is  straight  forward,  and  that  a  body  pro- 
jected into  open  space,  would  continue,  perpetually,  to  move 
in  a  right  line,  unless  retarded  or  drawn  out  of  this  course 
by  some  external  cause. 

797.  To  account  for  the  motions  of  the  planets  in  their 
orbits,  we  will  suppose  that  the  earth,  at  the  time  of  its  cre- 
ation, was  thrown  by  the  hand  of  the  Creator  into  open 
space,  the  sun  having  been  before  created  and  fixed  in  his 
present  place. 

798.  Under  Compound  Motion,  it  has  been  shown,  that 
when  a  body  is  acted  on  by  two  forces  perpendicular  to  each 
other,  its  motion  will  be  in  a  diagonal  line  between  the  di- 
rection of  the  two  forces. 

But  we  will  again  here  suppose  that  a  ball  be  moving 
in  the  line  m  x,  fig.  201,  with  a  given  force,  and  that 

Suppose  a  body  to  be  acted  on  by  two  forces  perpendicular  to  each 
other,  in  what  direction  will  it  move? 


ASTRONOMY. 


249 


Fig.  201.  another  force  half  as  great 

should  strike  it  in  the  direc- 
tion of  w,  the  ball  would 
then  describe  the  diagonal 
of  a  parallelogram,  whose 
length  would  be  just  equal 
to  twice  its  breadth,  and  the 
line  of  the  ball  would  be 
straight,  because  it  would  obey  the  impulse  and  direction 
of  these  two  forces  only. 

Fig.  202.  Now  let  a,  fig.  202, 

represent  the  earth,  and 
S  the  sun ;  and  suppose 
the  earth  to  be  moving 
forward,  in  the  line 
from  a  to  b,  and  to  have 
arrived  at  a,  with  a  ve- 
locity sufficient,  in  a 
given  time,  and  without 
disturbance,  to  have  car- 
ried it  to  b.  But  at  the 
point  a,  the  sun,  S,  acts 
upon  the  earth  with  his 
attractive  power,  and  with  a  force  which  would  draw  it  to  c, 
in  the  same  space  of  time  that  it  would  otherwise  have  gone 
to  b.  Then  the  earth,  instead  of  passing  to  b,  in  a  straight 
line,  would  be  drawn  down  to  d,  the  diagonal  of  the  parallel- 
ogram a,  b,  d,  c.  The  line  of  direction,  in  fig.  201,  is 
straight,  because  the  body  moved  obeys  only  the  direction 
of  the  two  forces,  but  it  is  curved  from  a  to  d,  fig.  202,  in 
consequence  of  the  continued  force  of  the  sun's  attraction, 
which  produces  a  constant  deviation  from  a  right  line. 

When  the  earth  arrives  at  d,  still  retaining  its  projectile 
or  centrifugal  force,  its  line  of  direction  would  be  towards  n, 
but  while  it  would  pass  along  to  n  without  disturbance,  the 
attracting  force  of  the  sun  is  again  sufficient  to  bring  it  to  e, 
in  a  straight  line,  so  that,  in  obedience  to  the  two  impulses, 
it  again  describes  the  curve  to  o. 

799.  It  must  be  remembered,  in  order  to  account  for  the 
circular  motions  of  the  planets,  that  the  attractive  force  of 
the  sun  is  not  exerted  at  once,  or  by  a  single  impulse,  as  is 

Why  does  the  ball,  fig.  201,  move  in  a  straight  linel  Why  does  the 
earth,  fig.  202,  move  in  a  curved  line  7  Explain  fig.  202,  and  show  how 
the  two  forces  act  to  produce  a  circular  line  of  motion  1 


250 


ASTRONOMY. 


the  case  with  the  cross  forces,  producing  a  straight  line,  nut 
that  this  force  is  imparted  by  degrees,  and  is  constant.  It 
therefore  acts  equally  on  the  earth,  in  all  parts  of  the  course 
from  a  to  d,  and  from  d  to  o.  From  0,  the  earth  having  the 
same  impulses  as  before,  it  moves  in  the  same  curved  or  cir- 
cular direction,  and  thus  its  motion  is  continued  perpetually. 

800.  The  tendency  of  the  earth  to  move  forward  in  a 
straight  line,  is  called  the  centrifugal  force,  and  the  attrac- 
tion of  the  sun,  by  which  it  is  drawn  downwards,  or  towards 
a  centre,  is  called  its  centripetal  force,  and  it  is  by  these  two 
forces  that  the  planets  are  made  to  perform  their  constant 
revolutions  around  the  sun. 

801.  In  the  above  explanation,  it  has  been  supposed  that 
the  sun's  attraction,  which  constitutes  the  earth's  gravity,  was 
at  all  times  equal,  or  that  the  earth  was  at  an  equal  distance 
from  the  sun,  in  all  parts  of  its  orbit.    But,  as  heretofore  ex- 
plained, the  orbits  of  all  the  planets  are  elliptical,  the  sun 
oeing  placed  in  the  lower  focus  of  the  eclipse.     The  sun's 

Fig.  203.  attraction    is,    therefore, 

stronger  in  some  parts  of 
their  orbits  than  in 
others,  and  for  this  rea- 
son their  velocities  are 
greater  at  some  periods 
of  their  revolutions  than 
at  others. 

To  make  this  under- 
stood, suppose,  as  before, 
that  the  centrifugal  and 
centripetal  forces  so  bal- 
ance each  other,  that  the 
earth  moves  round  the 
circular  orbit  a  e  b,  fig. 

^^^  203,  until  it  comes  to  the 

point  e ;  and  at  this  point,  let  us  suppose,  that  the  gravitating 
force  is  too  strong  for  the  force  of  projection,  so  that  the  earth, 
instead  of  continuing  its  former  direction  towards  b,  is  attract- 
ed by  the  sun  s,  in  the  curve  e  c.  When  at  c,  the  line  of  the 
earth's  projectile  force,  instead  of  tending  to  carry  it  farther 
from  the  sun,  as  would  be  the  case,  were  it  revolving  in  a  cir- 

What  is  the  projectile  force  of  the  earth  called?  What  is  the  attract 
ive  force  of  the  sun,  which  draws  the  earth  towards  him,  called!  Ex- 
plain fig.  203,  and  show  the  reason  why  the  velocity  is  increased  from 
c  to  d,  and  why  it  is  not  retarded  from  d  to  g  1 


ASTRONOMY. 


251 


cular  orbit,  now  tends  to  draw  it  still  nearer  to  him,  so  that  at 
this  point,  it  is  impelled  by  both  forces  towards  the  sun.  From 
<;,  therefore,  the  force  of  gravity  increasing  in  proportion  as 
the  square  of  the  distance  between  the  sun  and  earth  dimin- 
ishes, the  velocity  of  the  earth  will  be  uniformly  accelerated, 
until  it  arrives  at  the  point  nearest  the  sun,  d.  At  this  part  of 
us  orbit,  the  earth  will  have  gained,  by  its  increased  velocity, 
so  much  centrifugal  force,  as  to  give  it  a  tendency  to  over- 
come the  sun's  attraction,  and  to  fly  off  in  the  line  d  o.  But 
the  sun's  attraction  being  also  increased  by  the  near  approach 
of  the  earth,  the  earth  is  retained  in  its  orbit,  notwithstand- 
ing its  increased  centrifugal  force,  and  it  therefore  passes 
through  the  opposite  part  of  its  orbit,  from  d  to  g,  at  the 
same  distance  from  him  that  it  approached.  As  the  earth 
passes  from  the  sun,  the  force  of  gravity  tends  continually 
to  retard  its  motion,  as  it  did  to  increase  it  while  approach- 
ing him.  But  the  velocity  it  had  acquired  in  approaching 
the  sun,  gives  it  the  same  rate  of  motion  from  d  to  g,  that 
it  had  from  c  to  d.  From  g,  the  earth's  motion  is  uniformly 
retarded,  until  it  again  arrives  at  e,  the  point  from  which  it 
commenced,  and  from  whence  it  describes  the  same  orbit, 
by  virtue  of  the  same  forces,  as  before. 

The  earth,  therefore,  in  its  journey  round  the  sun,  moves 
at  very  unequal  velocities,  sometimes  being  retarded,  and 
then  again  accelerated,  by  the  sun's  attraction. 

802.  It   is  an    interesting   circumstance,  respecting   the 


Fig.  204. 


motions  of  the  planets,  that 
if  the  contents  of  their  or- 
bits be  divided  into  une- 
qual triangles,  the  acute 
angles  of  which  centre  at 
the  sun,  with  the  line  of 
the  orbit  for  their  bases, 
the  centre  of  the  planet 
will  pass  through  each  of 
these  bases  in  equal  times. 

This  will  be  understood 
by  fig.  204,  the  elliptical 
circle  being  supposed  to  be 
the  earth's  orbit,  with  the 
sun,  s,  in  one  of  the  foci. 

Now  the  spaces  1,  2,  3, 
&c.  though  of  different 


What  is  meant  by  a  planet's  passing  through  equal  spaces  in  equal  times  ? 


252  ASTRONOMY. 

shapes,  are  of  the  same  dimensions,  or  contain  the  same 
juantity  of  surface.  The  earth,  we  have  already  seen,  in 
its  journey  round  the  sun,  describes  an  ellipse,  and  moves 
more  rapidly  in  one  part  of  its  orhit  than  in  another.  But 
whatever  may  be  its  actual  velocity,  its  comparative  motion 
is  through  equal  areas  in  equal  times.  Thus  its  centre 
passes  from  E  to  C,  and  from  C  to  A,  in  the  same  period  of 
time,  and  so  of  all  the  other  divisions  marked  in  the  figure. 
If  the  figure,  therefore,  be  considered  the  plane  of  the  earth's 
orbit,  divided  in  12  equal  areas,  answering  to  the  12  months 
of  the  year,  the  earth  will  pass  through  the  same  areas  in 
every  month,  but  the  spaces  through  which  it  passes  will  be 
increased,  during  every  month,  for  one  half  the  year,  and 
diminished,  during  every  month,  for  the  other  half. 

803.  The  reason  why  the  planets,  when  they  approach 
near  the  sun,  do<  not  fall  to  him,  in  consequence  of  his  in- 
creased attraction,  and  why  they  do  not  fly  off  into  open 
space,  when  they  recede  to  the  greatest  distance  from  him, 
may  be  thus  explained. 

804.  Taking  the  earth  as  an  example,  we  have  shown 
that  when  in  the  part  of  her  orbit  nearest  the  sun,  her  velo- 
city is  greatly  increased  by  his  attraction,  and  that  conse- 
quently the  earth's  centrifugal  force  is  increased  in  propor- 
tion.    As  an  illustration  of  this,  we  know  that  a  thread 
which  will  sustain  an  ounce  ball,  when  whirled  round  in  the 
air,  at  the  rate  of  50  revolutions  in  a  minute,  would  be 
broken,  were  these  revolutions  increased  to  the  number  of 
60  or  70  in  a  minute,  and  that  the  ball  would  then  fly  off  jn 
a  straight  line.     This  shows  that  when  the  motion  of  a  re- 
volving body  is  increased,  its  centrifugal  force  is  also  in- 
creased.    Now,  the  velocity  of  the  earth  increases  in  an 
inverse  proportion,  as  its  distance  from  the  sun  diminishes. 
and  in  proportion  to  the  increase  of  velocity  is  its  centrifugal 
force  increased  ;  so  that,  in  any  other  part  of  its  orbit,  except 
when  nearest  the  sun,  this  increase  of  velocity  would  carry 
the  earth  away  from  its  centre  of  attraction.     But  this  in- 
crease of  the  earth's  velocity  is  caused  by  its  near  approach 
vO  the  sun,  and  consequently  the  sun's  attraction  is  increased, 
as  well  as  the  earth's  velocity.     In  other  terms,  when  the 

How  is  it  shown,  that  if  the  motion  of  a  revolving  body  is  increas- 
ed, its  projectile  force  is  also  increased  1  By  what  force  is  the  earth's  ve- 
Jocitv  increased,  as  it  approaches  the  sun  1  When  the  earth  is  nearest 
the  sun,  why  does  it  not  fall  to  him  7  When  the  earth's  centrifugal  forct 
is  greatest,  what  prevents  its  flying  to  the  sun  1 


EARTH.  253 

centrifugal  force  is  increased,  the  centripetal  force  is  in- 
creased in  proportion,  and  thus,  while  the  centrifugal  force 
prevents  the  earth  from  falling  to  the  sun,  the  centripetal 
force  prevents  it  from  moving  off  in  a  straight  line. 

805.  When  the  earth  is  in  that  part  of  its  orbit  most 
distant  from  the  sun,  its  projectile  velocity  being  retarded  by 
the  counter  force  of  the  sun's  attraction,  becomes  greatly 
diminished,  and  then  the  centripetal  force  becomes  stronger 
than  the  centrifugal,  and  the  earth  is  again  brought  back  by 
the  sun's  attraction,  as  before,  and  in  this  manner  its  motion 
goes  on  without  ceasing.     It  is  supposed,  as  the  planets 
move  through  spaces  void  of  resistance,  that  their  centrifugal 
forces  remain  the  same  as  when  they  first  emanated  from  the 
hand  of  the  Creator,  and  that  this  force,  without  the  influence 
of  the  sun's  attraction,  would  carry  them  forward  into  infinite 
space. 

THE  EARTH. 

806.  It  is  almost  universally  believed,  at  the  present  day, 
that  the  apparent  daily  motion  of  the  heavenly  bodies  from 
east  to  west,  is  caused  by  the  real  motion  of  the  earth  from 
west  to  east,  and  yet  there  are  comparatively  few  who  have 
examined  the  evidence  on  which  this  belief  is  founded.    For 
this  reason,  we  will  here  state  the  most  obvious,  and  to  a 
common  observer,  the  most  convincing  proofs  of  the  earth's 
revolution.     These  are,  first,  the  inconceivable  velocity  of 
the  heavenly  bodies,  and  particularly  the  fixed  stars  around 
the  earth,  if  she  stands  still.     Second,  the  fact,  that  all  as- 
tronomers of  the  present  age  agree  that  every  phenomenon 
which  the  heavens  present,  can  be  best  accounted  for,  by 
supposing  the  earth  to  revolve.     Third,  the  analogy  to  be 
drawn  from  many  of  the  other  planets,  which  are  known  to 
revolve  on  their  axis ;  and  fourth,  the  different  lengths  of 
days  and  nights  at  the  different  planets,  for  did  the  sun  re- 
volve about  the  solar  system,  the  days  and  nights  at  many 
of  the  planets  must  be  of  similar  lengths. 

807.  The  distance  of  the  sun  from  the  earth  being  95 
millions  of  miles,  the  diameter  of  the  earth's  orbit  is  twice 
its  distance  from  the  sun,  and,  therefore,  190  millions  of 
miles.     Now,  the  diameter  of  the  earth's  orbit,  when  seen 
from  the  nearest  fixed  star,  is  a  mere  point,  and  were  the 

What  are  the  most  obvious  and  convincing  proofs  that  the  earth  re- 
volves on  its  axis  1  Were  the  earth's  orbit  a  solid  mass,  could  it  be 
seen  by  us,  at  the  distance  of  the  fixed  stars  1 

22  ' 


254  EARTH, 

orbit  a  solid  mass  of  opaque  matter,  it  could  not  be  seen, 
with  such  eyes  as  ours,  from  such  a  distance.  This  is  known 
by  the  fact,  that  these  stars  appear  no  larger  to  us,  even 
when  our  sight  is  assisted  by  the  best  telescopes,  when  the 
earth  is  in  that  part  of  her  orbit  nearest  them,  than  when  at 
the  greatest  distance,  or  in  the  opposite  part  of  her  orbit. 
The  approach,  therefore,  of  190  millions  of  miles  towards 
the  fixed  stars,  is  so  small  a  part  of  their  whole  distance 
from  us,  that  it  makes  no  perceptible  difference  in  their  ap- 
pearance. Now,  if  the  earth  does  not  turn  on  her  axis  once 
in  24  hours,  these  fixed  stars  must  revolve  around  the  earth 
at  this  amazing  distance  once  in  24  hours.  If  the  sun 
passes  around  the  earth  in  24  hours,  he  must  travel  at  the 
rate  of  nearly  400,000  miles  in  a  minute  ;  but  the  fixed  stars 
are  at  least  400,000  times  as  far  beyond  the  sun,  as  the  sun 
is  from  us,  and,  therefore,  if  they  revolve  around  the  earth, 
must  go  at  the  rate  of  400,000  times  400,000  miles,  that  is, 
at  the  rate  of  160,000,000,000,  or  160  billions  of  miles  in  a 
minute ;  a  velocity  of  which  we  can  have  no  more  concep- 
tion than  of  infinity  or  eternity. 

808.  In  respect  to  the  analogy  to  be  drawn  from  the 
known  revolutions  of  the  other  planets,  and  the  different 
lengths  of  days  and  nights  among  them,  it  is  sufficient  to 
state,  that  to  the  inhabitants  of  Jupiter,  the  heavens  appear 
to  make  a  revolution  in  about  10  hours,  while  to  those  of 
Venus,  they  appear  to  revolve  once  in  23  hours,  and  to  the 
inhabitants  of  the  other  planets  a  similar  difference  seems 
to  take  place,  depending  on  the  periods  of  their  diurnal  re- 
volutions. Now,  there  is  no  more  reason  to  suppose  that 
the  heavens  revolve  round  us,  than  there  is  to  suppose  that 
the'y  revolve  around  any  of  the  other  planets,  since  the  same 
apparent  revolution  is  common  to  them  all;  and  as  we  know 
that  the  other  planets,  at  least  many  of  them,  turn  on  their 
axis,  and  as  all  the  phenomena  presented  by  the  earth,  can 
be  accounted  for  by  such  a  revolution,  it  is  folly  to  conclude 
otherwise. 


Suppose  the  earth  stood  still,  how  fast  must  the  sun  move  to  go 
round  it  in  24  hours  1  At  what  rate  must  the  fixed  stars  move  to  go 
round  the  earth  in  24  hours  1  If  the  heavens  appear  to  revolve  every 
10  hours  at  Jupiter,  and  every  24  hours  at  the  earth,  how  can  this  dif- 
ference be  accounted  for,  if  they  revolve  at  all  1  Is  there  any  more 
reason  to  believe  that  the  sun  revolves  round  the  earth,  than  round  any 
of  the  other  planets  1  How  can  all  the  phenomena  of  the  heavens  be 
accounted  for,  if  they  do  not  revolve  1 


EARTH. 


255 


Circles  and  Divisions  of  the  JEarth. 


809.  It  will  be  necessary  for  the  pupil  to  retain  in  his 
memory  the  names  and  directions  of  the  following  lines,  or 
circles,  by  which  the  earth  is  divided  into  parts.  These  lines 
it  must  be  understood,  are  entirely  imaginary,  there  being  no 
such  divisions  marked  by  nature  on  the  earth's  surface. 
They  are,  however,  so  necessary,  that  no  accurate  descrip- 
tion of  the  earth,  or  of  its  position  with  respect  to  the  hea 
venly  bodies,  can  be  conveyed  without  them. 

The  earth,  whose 
diameter  is  7912 
miles,  is  represented 
by  the  globe,  or 
sphere,  fig.  205. 
The  straight  line 
passing  thro'  its  cen- 
tre, and  about  which 
jj  it  turns,  is  called  its 
axis,  and  the  two  ex- 
tremities of  the  axis 
are  the  poles  of  the 
earth,  A  being  the 
north  pole,  and  B  the 
south  pole.  The 
line  C  D,  crossing 
the  axis,  passes  quite 
round  the  earth,  and  divides  it  into  two  equal  parts.  This 
is  called  the  equinoctial  line,  or  the  equator.  That  part  of 
the  earth,  situated  north  of  this  line,  is  called  the  northern, 
hemisphere,  and  that  part  south  of  it,  the  southern  hemi- 
sphere. The  small  circles  E  F,  and  G  H,  surrounding  or 
including  the  poles,  are  called  the  polar  circles.  That  sur- 
rounding the  north  pole  is  called  the  arctic  circle,  and  that  sur- 
rounding the  south,  the  antarctic  circle.  Between  these  cir- 
cles, there  is,  on  each  side  of  the  equator,  another  circle, 
which  marks  the  extent  of  the  tropics  towards  the  north  and 
south,  from  the  equator.  That  to  the  north  of  the  equator, 
I  K,  is  called  the  tropic  of  Cancer,  and  that  to  the  south, 
L  M,  the  tropic  of  Capricorn.  The  circle  L  K,  extending 

What  is  the  axis  of  the  earth  7  What  are  the  poles  of  the  earth  ? 
What  is  the  equator  1  Where  are  the  northern  and  southern  hemis- 
pheres 1  What  are  the  polar  circles  1  Which  is  the  arctic,  and  which 
the  antarctic  circle  7  Where  is  the  tropic  of  Cancer  and  where  the 
tropic  of  Capricorn  1 


256  EARTH. 

obliquely  across  the  two  tropics,  and  crossing  the  axis  of  the 
earth,  and  the  equator  at  their  point  of  intersection,  is  called 
the  ecliptic.  This  circle,  as  already  explained,  belongs 
rather  to  the  heavens  than  the  earth,  being  an  imaginary 
extension  of  the  plane  of  the  earth's  orbit  in  every  direction 
towards  the  stars.  The  line  in  the  figure,  shows  the  com- 
parative position  or  direction  of  the  ecliptic  in  respect  to  tht, 
equator,  and  the  axis  of  the  earth. 

The  lines  crossing  those  already  described,  and  meeting 
at  the  poles  of  the  earth,  are  called  meridian  lines,  or  mid- 
day lines,  for  when  the  sun  is  on  the  meridian  of  a  place,  it 
is  the  middle  of  the  day  at  that  place,  and  as  these  lines  ex- 
tend from  north  to  south,  the  sun  shines  on  the  whole  length 
of  each,  at  the  same  time,  so  that  it  is  12  o'clock,  at  the  same 
time,  on  every  place  situated  on  the  same  meridian. 

The  spaces  on  the  earth,  between  the  lines  extending  from 
east  to  west,  are  called  zones.  That  which  lies  between  the 
tropics,  from  M  to  K,  and  from  I  to  L,  is  called  the  torrid 
zone,  because  it  comprehends  the  hottest  portion  of  the 
earth.  The  spaces  which  extend  from  the  tropics,  north 
and  south,  to  the  polar  circles,  are  called  temperate  zones, 
because  the  climates  are  temperate,  and  neither  scorched 
with  heat,  like  the  tropics,  nor  chilled  with  cold,  like 
the  frigid  zones.  That  lying  north  of  the  tropic  of  Cancer, 
is  called  the  north  temperate  zone,  and  that  south  of  the 
tropic  of  Capricorn,  the  south  temperate  zone.  The  spaces 
included  within  the  polar  circles,  are  called  the  frigid 
zones.  The  lines  which  divide  the  globe  into  two  equal 
parts,  are  called  the  great  circles ;  these  are  the  ecliptic  and 
the  equator.  Those  dividing  the  earth  into  smaller  parts 
are  called  the  lesser  circles ;  these  are  the  lines  dividing  the 
tropics  from  the  temperate  zones,  and  the  temperate  zones 
from  the  frigid  zones,  &c. 

810.  Horizon. — The  horizon  is  distinguished  into  the. 
sensible  and  rational.  The  sensible  horizon  is  that  portion 
of  the  surface  of  the  earth  which  bounds  our  vision,  or  the 
circle  around  us,  where  the  sky  seems  to  meet  the  earth. 
When  the  sun  rises,  he  appears  above  the  sensible  horizon, 
and  when  he  sets,  he  sinks  below  it.  The  rational  horizon 

Wha>»is  the  ecliptic 7  What  are  the  meridian  lines'?  Or  ^.lav 
part  of  the  earth  is  the  torrid  zone  1  How  are  the  north  ar/  '.outt 
temperate  zones  bounded?  Where  are  the  frigid  zones  *?  "WKca  ar/ 
the  great,  and  which  the  lesser  circles  of  the  earth  1  How  Is  the  sensi  • 
ble  horizon  distinguished  from  the  rational  7 


EARTH.  '457 

is  ad  imaginary  line  passing  through  the  centre  of  the  earth, 
and  dividing  it  into  two  equal  parts. 

811.  Direction  of  the  Ecliptic. — The  ecliptic,  (758)  we 
have  already  seen,  is  divided  into  360  equal  parts,  called 
degrees.     All  circles,  however  large  or  small,  are  divided 
into  degrees,  minutes,  and  seconds,  in  the  same  manner  as 
the  ecliptic. 

812.  The  axis  of  the  ecliptic  is  an  imaginary  line  pass- 
ing through  its  centre  and  perpendicular  to  its  plane.     The 
extremities  of  this  perpendicular  line,  are  called  the  poles  of 
the  ecliptic. 

If  the  ecliptic,  or  great  plane  of  the  earth's  orbit,  be  con- 
sidered on  the  horizon,  or  parallel  with  it,  and  the  line  of 
the  earth's  axis  be  inclined  to  the  axis  of  this  plane,  or  the 
axis  of  the  ecliptic,  at  an  angle  of  23|  degrees,  it  will  repre- 
sent the  relative  positions  of  the  orbit,  and  the  axis  of  the 
earth.  These  positions  are,  however,  merely  relative,  for 
if  the  position  of  the  earth's  axis  be  represented  perpendicu- 
lar to  the  equator,  as  A  B,  fig.  205,  then  the  ecliptic  will 
cross  this  plane  obliquely,  as  in  that  figure.  But  when  the 
earth's  orbit  is  considered  as  having  no  inclination,  its  axis, 
of  course,  will  have  an  inclination,  to  the  axis  of  the  ecliptic, 
of  23£  degrees. 

As  the  tfrbits  of  all  the  other  planets  are  inclined  to  the 
ecliptic,  perhaps  it  is  the  most  natural  and  convenient  method 
to  consider  this  as  a  horizontal  plane,  with  the  equator  in- 
clined to  it,  instead  of  considering  the  equator  on  the  plane 
of  the  horizon,  as  is  sometimes  done. 

813.  Inclination  of  the  Earth1  s  axis. — The  inclination 
of  the  earth's  axis  to  the  axis  of  its  orbit  never  varies,  but 
always  makes  an  angle  with  it  of  23£  degrees,  as  it  moves 
round  the  sun.     The  axis  of  the  earth  is  therefore  always 
parallel  with  itself.     That  is,  if  a  line  be  drawn  through 
the  centre  of  the  earth,  in  the  direction  of  its  axis,  and  ex- 
tended north  and  south,  beyond  the  earth's  diameter,  the  line 
so  produced  will  always  be  parallel  to  the  same  line,  or  any 
number  of  lines,  so  drawn,  when  the  earth  is  in  different 
parts  of  its  orbit. 

How  are  circles  divided  1  What  is  the  axis  of  the  ecliptic  ?  What 
are  the  poles  of  the  ecliptic  7  How  many  degrees  is  the  axis  of  the  earth 
mclined  to  that  of  the  ecliptic  1  What  is  said  concerning  the  relative 
positions  of  the  earth's  axis  and  the  plane  of  the  ecliptic?  Are  the 
jrbits  of  the  other  planets  parallel  to  the  earth's  orbit,  or  inclined  to  itl 
What  is  meant  by  the  earth's  axis  being  parallel  to  itself  1 
23* 


258 


814.  Suppose  a  rod  to  be  fixed  V.j  the  flat  surface  of  a 
table,  and  so  inclined  as  to  make  e.<i  angle  with  a  perpen- 
dicular from  the  table  of  23£  degrees.  Let  this  rod  repre- 
sent the  axis  of  the  earth,  and  the  surface  of  the  table,  the 
ecliptic.  Now  place  on  the  table  a  lamp,  and  round  the 
lamp  hold  a  wire  circle  three  or  four  feet  in  diameter,  so 
that  it  shall  be  parallel  with  the  plane  of  the  table,  and  as 
high  above  it  as  the  flame  of  the  lamp.  Having  prepared 
a  small  terrestrial  globe,  by  passing  a  wire  through  it  for 
an  axis,  and  letting  it  project  a  few  inches  each  way,  for  the 
poles,  take  hold  of  the  north  pole,  and  carry  it  round  the 
circle,  with  the  poles  constantly  parallel  to  the  rod  rising 
above  the  table.  The  rod  being  inclined  23^  degrees  from 
a  perpendicular,  the  poles  and  axis  will  be  inclined  in  the 
same  degree,  and  thus  the  axis  of  the  earth  will  be  inclined 
to  that  of  the  ecliptic  every  where  in  the  same  degree,  and 
lines  drawn  in  the  direction  of  the  earth's  axis  will  be  paral- 
lel to  each  other  in  any  part  of  its  orbit. 
Fig.  206. 


\ 


This  will  be  understood  by  fig.  206,  where  it  will  be 
that  the  poles  of  the  earth,  in  the  several  positions  of  A,  B, 
C,  and  D,  being  equally  inclined,  are  parallel  to  each  other. 
Supposing  the  lamp  to  represent  the  sun,  and  the  wire  circle 
the  earth's  orbit,  the  actual  position  of  the  earth,  during  its 

How  does  it  appear  by  fig.  206,  that  the  axis  of  the  earth  is  parallel 
to  itself,  in  all  parts  of  its  orbit  1  How  are  the  annual  and  diurnal  re- 
Tolutions  of  the  earth  illustrated  by  fig.  20G. 


EARTH.  259 

annual  revolution  around  the  sun,  will  be  comprehended : 
and  if  the  globe  be  turned  on  its  axis,  while  passing  round 
the  lamp,  the  diurnal  or  daily  revolution  of  the  earth  will 
also  be  represented. 

DAY  AND  NIGHT. 

815.  Were  the  direction  of  the  earth's  axis  perpendicular 
to  the  plane  of  its  orbit,  the  days  and  nights  would  be  of 
equal  length  all  the  year,  for  then  just  one  half  of  the  earth, 
from  pole  to  pole,  would  be  enlightened,  and  at  the  same 
time  the  other  half  would  be  in  darkness. 
Pig.  207. 


Suppose  the  line  s  o,  fig.  207,  from  the  sun  to  the  earth, 
to  be  the  plane  of  the  earth's  orbit,  and  that  n  s,  is  the  axis 
of  the  earth  perpendicular  to  it,  then  it  is  obvious,  that  ex- 
actly the  same  points  on  the  earth  would  constantly  pass 
through  the  alternate  vicissitudes  of  day  and  night ;  for  all 
who  live  on  the  meridian  line  between  n  and  s,  which  line 
crosses  the  equator  at  0,  would  see  the  sun  at  the  same  time, 
and  consequently,  as  the  earth  revolves,  would  pass  into  the 
dark  hemisphere  at  the  same  time.  Hence  in  all  parts  of 
the  globe,  the  days  and  nights  would  be  of  equal  length,  at 
any  given  place. 

816.  Now  it  is  the  inclination  of  the  earth's  axis,  as  above 
described,  which  causes  the  lengths  of  the  days  and  nights 
to  differ  at  the  same  place  at  different  seasons  of  the  year, 
for  on  reviewing  the  position  of  the  globe  at  A,  fig.  206,  it 
will  be  observed,  that  the  line  formed  by  the  enlightened 
and  dark  hemispheres,  does  not  coincide  with  the  line  of  the 
axis  and  poles,  as  in  fig.  207,  but  that  the  line  formed  by 
the  darkness  and  the  light,  extends  obliquely  across  the  line 
of  the  earth's  axis,  so  that  the  north  pole  is  in  the  light, 
while  the  south  is  in  the  dark.  In  the  position  A,  there- 
fore, an  observer  at  the  north  pole  would  see  the  sun  con- 
Explain,  by  fig.  207,  why  the  days  and  nights  would  every  where 
be  equal,  were  the  axis  of  the  earth  perpendicular  to  the  plane  of  his 
orbit'?  What  is  the  cause  of  the  unequal  lengths  of  the  days  and  nighta 
in  different  parts  of  the  world  1 


260 


EARTH. 


stantly,  while  another  at  the  south  pole,  would  not  see  it  at 
all.  Hence  those  living  in  the  north  temperate  zone,  at  the 
season  of  the  year  when  the  earth  is  at  A,  or  in  the  summer, 
would  have  long  days  and  short  nights,  in  proportion  as  they 
approached  the  polar  circle ;  while  those  who  live  in  the 
south  temperate  zone,  at  the  same  time,  and  when  it  would 
be  winter  there,  would  have  long  nights  and  short  days  in 
the  same  proportion. 

SEASONS  OF  THE  YEAR. 

817.  The  vicissitudes  of  the  seasons  are  caused  by  the 
annual  revolution  of  the  earth  around  the  sun,  together  with 
the  inclination  of  its  axis  to  the  plane  of  its  orbit. 

It  has  already  been  explained,  that  the  ecliptic  is  the  plane 
of  the  earth's  orbit,  and  is  supposed  to  be  placed  on  a  level 
with  the  earth's  horizon,  and  hence,  that  this  plane  is  con- 
sidered the  standard,  by  which  the  inclination  of  the  lines 
crossing  the  earth,  and  the  obliquity  of  the  orbits  of  the  other 
planets,  are  to  be  estimated. 

818.  The  equinoctial  line,  or  the  great  circle  passing 
round  the  middle  of  the  earth,  is  inclined  to  the  ecliptic,  as 
well  as  the  line  of  the  earth's  axis,  and  hence  in  passing 
round  the  sun,  the 

equinoctial  line 
intersects,  or  cross- 
es the  ecliptic,  in 
two  places,  oppo- 
site to  each  other. 
Suppose  a  b,  fig. 
208,  to  be  the 
ecliptic,  e  f,  the 
equator,  and  c  d, 
the  earth's  axis. 
The  ecliptic  and 
equator  are  sup- 
posed to  be  seen 
edgewise,  so  as  to 
appear  like  lines  instead  of  circles.  Now  it  will  be  under- 
stood by  the  figure  that  the  inclination  of  the  equator  to  the 
ecliptic,  (or  the  sun's  apparent  annual  path  through  the 
heavens,)  will  cause  these  lines,  namely,  the  line  of  the  equa. 
tor  and  the  line  of  the  ecliptic,  to  cut,  or  cross  each  other, 

What  are  the  causes  which  produce  the  seasons  of  the  year  1     In 
what  position  is  the  equator,  with  respect  to  the  ecliptic  1 


EARTH.  261 

as  the  sun  makes  his  apparent  annual  revolution,  and  that 
this  intercession  will  happen  twice  in  the  year,  when  the 
earth  is  in  the  two  opposite  points  of  her  orbit. 

These  periods  are  on  the  21st  of  March,  and  the  21st  of 
September,  in  each  year,  and  the  points  at  which  the  sun  is 
seen  at  these  times,  are  called  the  equinoctial  points.  That 
which  happens  in  September  is  called  the  autumnal  equi- 
nox, and  that  which  happens  in  March,  the  vernal  equinox. 
At  these  seasons,  the  sun  rises  at  6  o'clock  and  sets  at  6 
o'clock,  and  the  days  and  nights  are  equal  in  length  in  every 
part  of  the  globe. 

819.  The  solstices  are  the  points  where  the  ecliptic  and 
the  equator  are  at  the  greatest  distance  from  each  other.    The 
earth,  in  its  yearly  revolution,  passes  through  each  of  these 
points.     One  is  called  the  summer,  and  the  other  the  winter 
solstice.     The  sun  is  said  to  enter  the  summer  solstice  on 
the  21st  of  June ;  and  at  this  time,  in  our  hemisphere,  the 
days  are  longest,  and  the  nights  shortest.     On  the  21st  of 
December,  he  enters  his  winter  solstice,  when  the  length  of 
the  days  and  nights  are  reversed  from  what  they  were  in 
June  before,  the  days  being  shortest,  and  the  nights  longest. 

Having  learned  these  explanations,  the  student  will  be 
able  to  understand  in  what  order  the  seasons  succeed  each 
other,  and  the  reason  why  such  changes  are  the  effect  of  the 
earth's  revolution. 

820.  Suppose  the  earth,  fig.  209,  to  be  in  her  summer 
solstice,  which  takes  place  on  the  21st  of  June.     At  this  pe- 
riod she  will  be  at  a,  having  her  north  pole,  n,  so  inclined 
towards  the  sun,  that  the  whole  arctic  circle  will  be  illumi- 
nated, and  consequently  the  sun's  rays  will  extend  23|  de- 
grees, the  breadth  of  the  polar  circles,  beyond  the  north 
pole.     The  diurnal  revolution,  therefore,  when  the  earth  is 
at  a,  causes  no  succession  of  day  and  night  at  the  pole,  since 
the  whole  frigid  zone  is  within  the  reach  of  his  rays.     The 
people  who  live  within  the  arctic  circle  will,  consequently, 
at  this  time,  enjoy  perpetual  day.     During  this  period,  just 

At  what  times  in  the  year  do  the  line  of  the  ecliptic  and  that  of  the 
equinox  intersect  each  other*?  What  are  these  points  of  intersection 
called  1  Which  is  the  autumnal,  and  which  the  vernal  equinox  1  At 
what  time  does  the  sun  rise  and  set,  when  he  is  in  the  equinoxes  ? 
What  are  the  solstices  7  When  the  sun  enters  the  summer  solstice, 
•what  is  said  of  the  length  of  the  days  and  nights  1  When  does  the 
sun  enter  the  winter  solstice,  and  what  is  the  proportion  between  the 
length  of  the  days  and  nights  1  At  what  season  of  the  year  is  the 
whole  arctic  circle  illuminated  7 


262  EARTH. 

Fig.  209. 


Y  *\ 

'•» 

SKSrn  SS IS™ 

Hemisphere  ^ff       Hemisphere  WM 

V 


the  same  proportion  of  the  earth  that  is  enlightened  in  the 
northern  hemisphere,  will  be  in  total  darkness  in  the  oppo- 
site region  of  the  southern  hemisphere;  so  that  while  the 
people  of  the  north  are  blessed  with  perpetual  day,  those  *of 
the  south  are  groping  in  perpetual  night.  Those  who  live 
near  the  arctic  circle  in  the  north  temperate  zone,  will,  du- 
ring the  winter,  come,  for  a  few  hours,  within  the  regions  of 
night,  by  the  earth's  diurnal  revolution ;  and  the  greater  the 
distance  from  the  circle,  the  longer  will  be  their  nights,  and 
the  shorter  their  days.  Hence,  at  this  season,  the  days  will 
be  longer  than  the  nights  everywhere  between  the  equator 
and  the  arctic  circle.  At  the  equator,  the  days  and  nights 
will  be  equal,  and  between  the  equator  and  the  south  polar 
circle,  the  nights  will  be  longer  than  the  days,  in  the  same 
proportion  as  the  days  are  longer  than  the  nights,  from  the 
equator  to  the  arctic  circle. 

As  the  earth  moves  round  the  sun,  the  line  which  divides 
the  darkness  and  the  light,  gradually  approaches  the  poles, 
till  having  performed  one  quarter  of  her  yearly  journey 
from  the  point  a,  she  comes  to  b,  about  the  21st  of  Sep- 
tember. At  this  time,  the  boundary  of  light  and  darkness 

At  what  season  is  the  whole  antarctic  circle  in  the  dark  1  While 
the  people  near  the  north  pole  enjoy  perpetual  day,  what  is  the  situa- 
tion of  those  near  the  south  pole  7  At  what  season  will  the  days  be 
longer  than  the  nights  everywhere  between  ihe  equator  and  the  arctic 
circle  1  At  what  season  will  the  nights  be  longer  than  the  days  in  the 
southern  hemisphere  1  When  will  the  days  and  nights  be  equal  in  aU 
parts  of  the  earth  1 


EARTH.  263 

passes  through  the  poles,  dividing  the  earth  equally  from 
east  to  west ;  and  thus  in  every  part  of  the  world,  the  days 
and  nights  are  of  equal  length,  the  sun  being  12  hours  al- 
ternately above  and  below  the  horizon.  In  this  position  of 
*he  earth,  the  sun  is  said  to  be  in  the  autumnal  equinox. 

In  the  progress  of  the  earth  from  b  to  c,  the  light  of  the 
sun  gradually  reaches  a  little  more  of  the  antarctic  circle. 
The  days,  therefore,  in  the  northern  hemisphere,  grow 
shorter  at  every  diurnal  revolution,  until  the  21st  of  De- 
cember, when  the  whole  arctic  circle  is  involved  in  total 
darkness.  And  now,  the  same  places  which  enjoyed  con- 
stant day  in  the  June  before,  are  involved  in  perpetual  night. 
At  this  time,  the  sun,  to  those  who  live  in  the  northern  hemi- 
sphere, is  said  to  be  in  his  winter  solstice ;  and  then  the 
winter  nights  are  just  as  long  as  were  the  summer  days, 
and  the  winter  days  as  long  as  the  summer  nights. 

When  the  earth  has  ^one  another  quarter  of  her  annual 
journey,  and  has  come  to  the  point  of  her  orbit  opposite  to 
where  she  was  on  the  21st  of  September,  which  happens  on 
the  21st  of  March,  the  line  dividing  the  light  from  the  dark- 
ness again  passes  through  both  poles.  In  this  position  of 
the  earth  with  respect  to  the  sun,  the  days  and  nights  are 
again  equal  all  over  the  world,  and  the  sun  is  said  to  be  in 
his  vernal  equinox. 

From  the  vernal  equinox,  as  the  earth  advances,  the 
northern  hemisphere  enjoys  more  and  more  light,  while  the 
southern  falls  into  the  region  of  darkness,  in  proportion,  so 
that  the  days  north  of  the  equator  increase  in  length,  until 
the  21st  of  June,  at  which  time,  the  sun  is  again  longest 
above  the  horizon,  and  the  shortest  time  below  it. 

821.  Thus  the  apparent  motion  of  the  sun  from  east  to 
west,  is  caused  by  the  real  motion  of  the  earth  from  west  to 
east.  If  the  earth  is  in  any  point  of  its  orbit,  the  sun  will 
always  seem  in  the  opposite  point  in  the  heavens.  When 
the  earth  moves  one  degree  to  the  west,  the  sun  seems  to 
move  the  same  distance  to  the  east ;  and  when  the  earth  has 
completed  one  revolution  in  its  orbit,  the  sun  appears  to 
have  completed  a  revolution  through  the  heavens.  Hence 
it  follows,  that  the  ecliptic,  or  the  apparent  path  of  the  sun 

At  what  season  of  the  year  is  the  whole  arctic  circle  involved  in 
darkness  1  When  are  the  days  and  nights  equal  all  over  the  world1? 
When  is  the  sun  in  the  vernal  equinox  7  What  is  the  cause»of  the  ap- 
parent motion  of  the  sun  from  east  to  west?  What  is  the  apparent 
path  of  the  sun,  but  the  real  path  of  the  earth  1 


264  SEASONS. 

through  the  heavens,  is  the  real  path  of  the  earth  round 
the  sun. 

822.  It  will  be  observed  by  a  careful  perusal  of  the  above 
explanation  of  the  seasons,  and  a  close  inspection  of  the  fig- 
ure by  which  it  is  illustrated,  that  the  sun  constantly  shines 
on  a  portion  of  the  earth  equal  to  90  degrees  north,  and  90 
degrees  south,  from  his  place  in  the  heavens,  and,  conse- 
quently, that  he  always  enlightens  180  degrees,  or  one  half 
of  the  earth.     If,  therefore,  the  axis  of  the  earth  were  per- 
pendicular to  the  plane  of  its  orbit,  the  days  and  nights 
would  everywhere  be  equal,  for  as  the  earth  performs  its 
diurnal  revolutions,  there  would  be   12  hours  day,  and  12 
hours  night.     But  since  the  inclination  of  its  axis  is  23-i 
degrees,  the  light  of  the  sun  is  thrown  23£  degrees  beyond 
the  north  pole ;  that  is,  it  enlightens  the  earth  23^  degrees 
further  in  that  direction,  when  the  north  pole  is  turned  to- 
wards the  sun,  than  it  would,  had  the  earth's  axis  no  incli- 
nation.    Now,  as  the  sun's  light  reaches  only  90  degrees 
north  or  south  of  his  place  in  the  heavens,  so  when  the  arc- 
tic circle  is  enlightened,  the  antarctic  circle  must  be  in  the 
dark ;  for  if  the  light  reaches  23-|  degrees  beyond  the  north 
pole,  it  must  fall  23|  degrees  short  of  the  south  pole. 

823.  As  the  earth  travels  round  the  sun,  in  his  yearly 
circuit,  this  inclination  of  the  poles  is  alternately  towards 
and  from  him.     During  our  winter,  the  north  polar  region 
is  thrown  beyond  the  rays  of  the  sun,  while  a  correspond- 
ing portion  around  the  south  pole  enjoys  the  sun's  light. 
And  thus,  at  the  poles,  there  are  alternately  six  months  of 
darkness  and  winter,  .and  six  months  of  sunshine  and  sum- 
mer.    While  we,  in  the  northern  hemisphere,  are  chilled 
by  the  cold  blasts  of  winter,  the  inhabitants  of  the  southern 
hemisphere  are  enjoying  all  the  delights  of  summer ;  and 
while  we  are  scorched  by  the  rays  of  a  vertical  sun  in  June 
and  July,  our  southern  neighbours  are  shivering  with  the 
rigours  of  mid-winter. 

At  the  equator,  no  such  changes  take  place.  The  rays 
of  the  sun,  as  the  earth  passes  round  him,  are  vertical  twice 
a  year  at  every  place  between  the  tropics.  Hence,  at  the 


Had  the  earth's  axis  no  inclination,  why  would  the  days  and  nights 
always  be  equal  1  How  many  degrees  does  the  sun's  light  reach,  north 
and  south  of  him,  on  the  earth?  During  our  winter,  is  the  north  pole 
turned  to  or  from  the  sun  ?  At  the  poles,  how  many  days  and  nights 
are  there  in  the  year?  When  it  is  winter  in  the  northern  hemisphere, 
what  is  the  season  in  the  southern  hemisphere'? 


SEASONS.  265 

equator,  there  are  two  summers  and  no  winter,  and  as  the 
sun  there  constantly  shines  on  the  same  half  of  the  earth  in 
succession,  the  days  and  nights  are  always  equal,  there  being 
12  hours  of  light,  and  12  of  darkness. 

824.  MOTION  OF  THE  EARTH. — The  motion  of  the  earth 
round  the  sun,  is  at  the  rate  of  68,000  miles  in  an  hour, 
while  its  motion  on  its  own  axis,  at  the  equator,  is  at  the 
rate  of  about  1042  miles  in  the  hour.     The  equator,  being 
that  part  of  the  earth  most  distant  from  its  axis,  the  motion 
there  is  more  rapid  than  towards  the  poles,  in  proportion  to 
its  greater  distance  from  the  axis  of  motion.     See  fig.  16. 
(174.) 

825.  The  method  of  ascertaining  the  velocity  of  the  earth's 
motion,  both  in  its  orbit  and  round  its  axis,  is  simple,  and 
easily  understood ;  for  by  knowing  the  diameter  of  the  earth's 
orbit,  its  circumference  is  readily  found,  and  as  we  know 
how  long  it  takes  the  earth  to  perform  her  yearly  circuit, 
we  have  only  to  calculate  what  part  of  her  journey  she  goes 
through  in  an  hour.     By  the  same  principle,  the  hourly 
rotation  of  the  earth  is  as  readily  ascertained. 

We  are  insensible  to  these  motions,  because  not  only  the 
earth,  but  the  atmosphere,  and  all  terrestrial  things,  partake 
of  the  same  motion,  and  there  is  no  change  in  the  relation 
of  objects  in  consequence  of  it.  If  we  look  out  at  the  win- 
dow of  a  stearn-boat,  when  it  is  in  motion,  the  boat  will  seem 
to  stand  still,  while  the  trees  and  rocks  on  the  shore  appear 
to  pass  rapidly  by  us.  This  deception  arises  from  our  not 
having  any  object  with  which  to  compare  this  motion,  when 
shut  up  in  the  boat;  for  then  every  object  around  us  keeps 
the  same  relative  position.  And  so,  in  respect  to  the  motion 
of  the  earth,  having  nothing  with  which  to  compare  its 
movement,  except  the  heavenly  bodies,  when  the  earth  moves 
in  one  direction,  these  objects  appear  to  move  in  the  con- 
trary direction. 

CAUSES  OF  THE  HEAT  AND  COLD*  OF  THE  SEASONS. 

826.  We  have  seen  that  the  earth  revolves  round  the  sun 
in  an  elliptical  orbit,  of  which  the  sun  is  one  of  the  foci,  and 
consequently,  that  the  earth  is  nearest  him,  in  one  part  of 
her  orbit  than  in  another.     From  the  great  difference  we 

At  what  rate  does  the  earth  move  around  the  sun  1    How  fast  does 
it  move  around  its  axis  at  the  equator?    How  is  the  velocity  of  the 
earth  ascertained  "?    Why  are  we  insensible  of  the  earth's  motion  7 
23 


266  SEASONS. 

experience  between  the  heat  of  summer  and  that  of  winter, 
we  should  be  led  to  suppose  that  the  earth  must  be  much 
nearer  the  sun  in  the  hot  season  than  in  the  cold.  But  when 
we  come  to  inquire  into  this  subject,  and  to  ascertain  the  dis- 
tance of  the  sun  at  different  seasons  of  the  year,  we  find  that 
the  great  source  of  heat  and  light  is  nearest  us  during  the 
cold  of  winter,  and  at  the  greatest  distance  during  the  hear 
of  summer. 

827.  It  has  been  explained,  under  the  article  Optics,  thai 
the  angle  of  vision  depends  on  the  distance  at  which  a  body 
of  given  dimensions  is  seen.     Now,  on  measuring  the  an- 
gular dimension  of  the  sun,  with  accurate  instruments,  at 
different  seasons  of  the  year,  it  has  been  found  that  his  di- 
mensions increase  and  diminish,  and  that  these  variations 
correspond   exactly  with   the    supposition,  that    the  earth 
moves  in  an  elliptical  orbit.     If,  for  instance,  his  apparent 
diameter  be  taken  in  March,  and  then  again  in  July,  it  will 
be  found  to  have  diminished,  which  diminution  is  only  to 
be  accounted  for,  by  supposing  that  he  is  at  a  greater  dis- 
tance from  the  observer  in  July  than   in  March.     From 
July,  his  angular  diameter  gradually  increases,  till  January, 
when  it  again  diminishes,  and   continues  to  diminish,  until 
July.     By  many  observations,  it  is  found,  that  the  greatest 
apparent  diameter  of  the  sun,  and  therefore  his  least  distance 
from  us,  is  in  January,  and  his  least  diameter,  and  there- 
fore his  greatest  distance,  is  in  July.     The  actual  difference 
is  about  three  millions  of  miles,  the  sun  being  that  distance 
further  from  the  earth  in  July  than   in  January.      This, 
however,  is  only  about  one  sixtieth  of  his  mean  distance 
from  us,  and  the  difference  we  should  experience  in  his 
heat,  in  consequence  of  this  difference  of  distance,  will  there- 
fore be  very  small.     Perhaps  the  effect  of  his  proximity  to 
the  earth  may  diminish,  in  some  small  degree,  the  severity 
of  winter. 

828.  The  heat  of  summer,  and  the'  cold  of  winter,  must 
therefore  arise  from  the  difference  in  the  meridian  altitude 
of  the  sun,  and  in  the  time  of  his  continuance  above  the 

At  what  season  of  the  year  is  the  sun  at  the  greatest,  and  at  what 
season  the  least  distance,  from  the  earth  1  How  is  it  ascertained  that 
the  earth  moves  in  an  elliptical  orbit,  by  the  appearance  of  the  sun  1 
When  does  the  sun  appear  under  the  greatest  apparent  diameter,  and 
when  under  the' least?  How  much  farther  is  the  sun  from  us  in  July 
than  in  January?  What  effect  does  this  difference  produce  on  the 
earth  ?  How  is  the  heat  of  summer,  and  the  cold  of  winter,  account- 
ed for? 


SEASONS. 


267 


horizon.  In  summer,  the  solar  rays  fall  on  the  earth,  in 
nearly  a  perpendicular  direction,  and  his  powerful  heat  is 
then  constantly  accumulated  by  the  long  days  and  short 
nights  of  the  season.  In  winter,  on  the  contrary,  the  solar 
ravs  fall  so  obliquely  on  the  earth,  as  to  produce  little 
warmth,  and  the  small  effect  they  do  produce  during  the 
short  days  of  that  season,  is  almost  entirely  destroyed  by  the 
long  nights  which  succeed.  The  difference  between  the 
effects  of  perpendicular  and  oblique  rays,  seems  to  depend, 
in  a  great  measure,  on  the  different  extent  of  surface  over 
which  they  are  spread.  When  the  rays  of  the  sun  are  made 
to  pass  through  a  convex  lens,  the  heat  is  increased,  because 
the  number  of  rays  which  naturally  covered  a  large  surface, 
are  then  made  to  cover  a  smaller  one,  so  that  the  power  of 
the  glass  depends  on  the  number  of  rays  thus  brought  to  a 
focus.  If,  on  the  contrary,  the  rays  of  the  sun  are  suffered 
to  pass  through  a  concave  lens,  their  natural  heating  power 
is  diminished,  because  they  are  dispersed,  or  spread  over  a 
wider  surface  than  before. 

829.  Now,  to  apply  these  different  effects  to  the  summer 
and  winter  rays  of  the  sun,  let  us  suppose  that  the  rays  fall- 
ing perpendicularly 
on  a  given  extent  of 
surface,  impart  to  it  a 
certain  degree  of  heat, 
then  it  is  obvious,  that 
if  the  same  number  of 
rays  be  spread  over 
twice  that  extent  of 
surface,  their  heating 
power  would  be  di- 
minished in  propor- 
tion, and  that  only  half 
the  heat  would  be  im- 
parted. This  is  the 
effect  produced  by  the 
sun's  rays  in  the  win- 
ter. They  fall  so  obliquely  on  the  earth,  as  to  occupy  near- 
ly double  the  space  that  the  same  number  of  rays  do  in  the 
summer. 

Why  do  the  perpendicular  rays  of  summer  produce  greater  effects 
than  the  oblique  rays  of  winter  1  How  is  this  illustrated  by  the  con- 
vex and  concave  lenses  1  How  is  the  actual  difference  of  the  summer 
and  winter  rays  shown  1 


Fig.  210. 


268  FIGURE  OB1  THE  EARTH. 

This  is  illustrated  by  fig.  210,  where  the  number  of  rays, 
both  in  winter  and  summer,  are  supposed  to  be  the  same, 
But,  it  will  be  observed,  that  the  winter  rays,  owing  to  their 
oblique  direction,  are  spread  over  nearly  twice  as  much  sur- 
face as  those  of  summer. 

830.  It  may,  however,  be  remarked,  that  the  hottest  sea- 
son is  not  usually  at  the  exact  time  of  the  year,  when  the 
sun  is  most  vertical,  and  the  days  the  longest,  as  is  the  case 
towards  the  end  of  June,  but  some  time  afterwards,  as  in 
July  and  August. 

To  account  for  this,  it  must  be  remembered,  that  when 
the  sun  is  nearly  vertical,  the  earth  accumulates  more  heat 
by  day  than  it  gives  out  at  night,  and  that  this  accumulation 
continues  to  increase  after  the  days  begin  to  shorten,  and, 
consequently,  the  greatest  elevation  of  temperature  is  some 
time  after  the  longest  days.  For  the  same  reason,  the  ther- 
mometer generally  indicates  the  greatest  degree  of  heat  at 
two  or  three  o'clock  on  each  day,  and  not  at  twelve  o'clock, 
when  the  sun's  rays  are  most  powerful. 

FIGURE  OF  THE  EARTH. 

831.  Astronomers  have  proved  that  all  the  planets,  to- 
gether with  their  satellites,  have  the  shape  of  the  sphere,  or 
globe,  and  hence,  by  analogy,  there  was  every  reason  to 
suppose,  that  the  earth  would  be  found  of  the  same  shape ; 
and  several  phenomena  tend  to  prove,  beyond  all  doubt,  that 
this  is  its  form.     The  figure  of  the  earth  is  not,  however, 
exactly  that  of  a  globe,  or  ball,  because  its  diameter  is  about 
34  miles  less  from  pole  to  pole,  than  it  is  at  the  equator. 
But  that  its  general  figure  is  that  of  a  sphere,  or  ball,  is 
proved  by  many  circumstances. 

832.  When  one  is  at  sea,  or  standing  on  the  seashore, 
the  first  part  of  a  ship  seen  at  a  distance,  is  its  mast.     As 
the  vessel  advances,  the  mast  rises  higher  and  higher  above 
the  horizon,  and  finally  the  hull,  and  whole  ship,  become 
visible.     Now,  were  the  earth's  surface  an  exact  plane,  no 
such  appearance  would  take  place,  for  we  should  then  see 
the  hull  long  before  the  mast  or  rigging,  because  it  is  much 
the  largest  object. 

Why  is  not  the  hottest  season  of  the  year  at  the  period  when  the 
days  are  longest,  and  the  sun  most  vertical  1  What  is  the  general  fig- 
ure of  the  earth  1  How  much  less  is  the  diameter  of  the  earth  at  the 
poles  than  at  the  equator  7  How  is  the  convexity  of  the  earth  proved, 
by  the  approach  of  a  ship  at  sea  7 


FIGURE  OF  THE  EARTH.  269 

Fig.  211. 

TheEartTis&invzxity 


a 

It  will  be  plain  by  fig.  211,  that  were  the  ship,  a,  eleva- 
ted, so  that  the  hull  should  be  or*  a  horizontal  line  with  the 
eye,  the  whole  ship  would  be  visible,  instead  of  the  topmast, 
there  being1  no  reason,  except  the  convexity  of  the  earth,  why 
the  whole  ship  should  not  be  visible  at  a,  as  well  as  at  b. 

We  know,  for  the  same  reason,  that  in  passing  over  a 
hill,  the  tops  of  the  trees  are  seen,  before  we  can  discover 
the  ground  on  which  they  stand ;  and  that  when  a  man  ap- 
proaches from  the  opposite  side  of  a  hill,  his  head  is  seen 
before  his  feet. 

It  is  a  well  known  fact  also,  that  navigators  have  set  out 
from  a  particular  port,  and  by  sailing  continually  westward, 
have  .passed  around  the  earth,  and  again  reached  the  port 
from  which  they  sailed.  This  could  never  happen,  were 
the  earth  an  extended  plain,  since  then  the  longer  the  navi- 
gator sailed  in  one  direction,  the  further  he  would  be  from 
home. 

Another  proof  of  the  spheroidal  form  of  the  earth,  is  the 
figure  of  its  shadow  on  the  moon,  during  eclipses,  which 
shadow  is  always  bounded  by  a  circular  line. 

These  circumstances  prove  beyond  all  doubt,  that  the 
form  of  the  earth  is  globular,  but  that  it  is  not  an  exact 
sphere;  and  that  it  is  depressed  or  flattened  at  the  poles,  is 
shown  by  the  difference  in  the  lengths  of  pendulums  vibra- 
ting seconds  at  the  poles,  and  at  the  equator. 

833.  Under  the  article  pendulum,  it  was  shown  that  its 
vibrations  depend  on  the  attraction  of  gravitation,  and  that  as 
:he  centre  of  the  earth  is  the  centre  of  this  attraction,  so  the 
nearer  this  instrument  is  carried  to  that  point,  the  stronger 
will  be  the  attraction,  and  consequently  the  more  frequent 
its  vibrations. 

From  a  great  number  of  experiments,  it  has  been  found 

Explain  fig.  211.  What  other  proofs  of  the  globular  shape  of  the 
earth  are  mentioned  1  How  is  it  proved  by  the  vibrations  of  the  pen- 
dulum, that  the  earth  is  flattened  at  the  poles  7 


270 


FIGURE  OP  THE  EARTH, 


that  a  pendulum,  which  vibrates  seconds  at  the  equator,  has 
its  number  of  vibrations  increased,  when  it  is  carried  to- 
wards the  poles ;  and  as  its  number  of  vibrations  depends 
upon  its  length,  a  clock  which  keeps  accurate  time  at  the 
equator,  must  have  its  pendulum  lengthened  at  the  poles. 
And  so,  on'the  contrary,  a  clock  going  correctly  at,  or  near 
the  poles,  must  have  its  pendulum  shortened,  to  keep  exac* 
time  at  the  equator.  Hence  the  force  of  gravity  is  greates 
at  the  poles,  and  least  at  the  equator. 

The  manner  in  which 
the  figure  of  the  earth  dif- 
fers from  that  of  a  sphere, 
is  represented  by  fig.  212, 
where  n  is  the  north  pole, 
and  s  the  south  pole,  the  line 
from  one  of  these  points  to 
the  other,  being  the  axis  of 
the  earth,  and  the  line  cross- 
ing this,  the  equator.  It  will 
be  seen  by  this  figure,  that 
the  surface  of  the  earth,  at 
the  poles,  is  nearer  its  centre, 
than  the  surface  at  the  equa- 
tor. The  actual  difference  between  the  polar  and  equatorial 
diameters  is  in  the  proportion  of  300  to  301.  The  earth  is 
therefore  called  an  oblate  spheroid,  the  word  oblate  signify* 
ing  the  reverse  of  oblong,  or  shorter  in  one  direction  than 
in  another. 

834.  The  compression  of  the  earth  at  the  poles,  and  the' 
consequent  accumulation  of  matter  at  the  equator,  is  proba- 
bly the  effect  of  its  diurnal  revolution,  while  it  was  in  a  soft 
or  plastic  state.  If  a  ball  of  soft  clay,  or  putty,  be  made  to 
revolve  rapidly,  by  means  of  a  stick  passed  through  its  cen- 
tre, as  an  axis,  it  will  swell  out  in  the  middle,  or  equator, 
and  be  depressed  at  the  poles,  assuming  the  precise  figure 
of  the  earth.  This  figure  is  the  natural  and  obvious  conse- 
quence of  the  centrifugal  force,  which  operates  to  throw  the 
matter  of£  in  proportion  to  its  distance  from  the  axis  of  mo* 
tion,  and  the  rapidity  with  which  the  ball  is  made  to  revolve. 

In  what  proportion  is  the  polar  less  than  the  equatorial  diameter'? 
What  is  the  earth  called,  in  reference  to  this '  figure  7  How  is  it  sup- 
posed that  it  came  to  have  this  form  1  How  is  the  form  of  the  earth  il- 
lustrated by  experiment  7  Explain  the  reason  why-  a  plastic  ball  will 
swell  at  the  equator^  when  made  to  revolve, 


TIME.  271 

The  parts  about  the  equator  would  therefore  tend  to  fly  off) 
and  leave  the  other  parts,  in  consequence  of  the  centrifugal 
force,  while  those  about  the  poles,  being  near  the  centre  of 
motion,  would  receive  a  much  smaller  impulse.  Conse- 
quently, the  ball  would  swell,  or  bulge  out  at  the  equator, 
which  would  produce  a  corresponding  depression  at  the 
poles. 

835.  The  weight  of  a  body  at  the  poles  is  found  to  be 
greater  than  at  the  equator,  not  only  because  the  poles  are 
nearer  the  centre  of  the  earth  than  the  equator,  but  because 
the  centrifugal  force  there  tends  to  lessen  its  gravity.     The 
wheels  of  machines,  which  revolve  with  the  greatest  rapid- 
ity, are  made  in  the  strongest  manner,  otherwise  they  will 
fly  in  pieces,  the  centrifugal  force  not  only  overcoming  the 
gravity,  but  the  cohesion  of  their  parts. 

836.  It  has  been  found,  by  calculation,  that  if  the  earth 
turned  over  once  in  84  minutes  and  43  seconds,  the  centrifu- 
gal force  at  the  equator  would  be  equal  to  the  power  of 
gravity  there,  and  that  bodies  would  entirely  lose   their 
weight.     If  the  earth  revolved  more  rapidly  than  this,  all 
the  buildings,  rocks,  mountains,  and  men,  at  the  equator, 
would  not  only  lose  their  weight,  but  would  fly  away,  and 
leave  the  earth. 

SOLAR  AND  SIDERIAL  TIME, 

836.  The  stars  appear  to  go  round  the  earth  in  23  hours, 
56  minutes,  and  4  seconds,  while  the  sun  appears  to  per- 
form the  same  revolution  in  24  hours,  so  that  the  stars  gain 
3  minutes  and  56  seconds  upon  the  sun  every  day.  In  a  year, 
this  amounts  to  a  day,  or  to  the  time  taken  by  the  earth  to 
perform  one  diurnal  revolution.  It  therefore  happens,  that 
when  time  is  measured  by  the  stars,  there  are  366  days  in 
the  year,  or  366  diurnal  revolutions  of  the  earth ;  while,  if 
measured  by  the  sun  from  one  meridian  to  another,  there 
are  only  365  whole  days  in  the  year.  The  former  are  call- 
ed the  siderial,  and  the  latter  solar  days. 

To  account  for  this  -difference,  we  must  remember  that 
the  earth,  while  she  performs  her  daily  revolutions,  is  con- 
stantly advancing  in  her  orbit,  and  that,  therefore,  at  12 

What  two  causes  render  the  weights  of  bodies  less  at  the  equator 
« Jian  at  the  poles  1  What  would  be  the  consequence  on  the  weights  of 
bodies  ft  the  equator,  did  the  earth  turn  over  once  in  84  minutes  and 
43  seconds  1  The  stars  appear  to  move  round  the  earth  in  less  time  than, 
the  sun,  v.'hat  does  the  d  ifference  amount  to  in  a  year  1  What  is  the  yea» 
meascreJ  )••"  *  itn.r  railed  ?  What  is  that  measured  bv  the  sun  called  * 


272  TIME. 

o'clock  to-day  she  is  not  precisely  at  the  same  place  in  re- 
spect  to  the  sun,  that  she  was  at  12  o'clock  yesterday,  or  will 
be  to-morrow.  But  the  fixed  stars  are  at  such  an  amazing- 
distance  from  us,  that  the  earth's  orbit,  in  respect  to  them,  is 
but  a  point ;  and,  therefore,  as  the  earth's  diurnal  motion  is 
perfectly  uniform,  she  revolves  from  any  given  star  to  the 
same  star  again,  in  exactly  the  same  period  of  absolute  time. 
The  orbit  of  the  earth,  were  it  a  solid  mass,  instead  of  an 
imaginary  circle,  would  have  no  appreciable  length  or 
breadth,  when  seen  from  a  fixed  star,  and  therefore,  whether 
the  earth  performed  her  diurnal  revolutions  at  a  particular 
station,  or  while  passing  round  in  her  orbit,  would  make  no 
appreciable  difference  with  respect  to  the  star.  Hence  the 
same  star,  at  every  complete  daily  revolution  of  the  earth, 
appears  precisely  in  the  same  direction  at  all  seasons  of  the 
year.  The  moon,  for  instance,  would  appear  at  exactly  the 
same  point,  to  a  person  who  walks  round  a  circle  of  a  hun- 
dred yards  in  diameter,  and  for  the  same  reason  a  star  ap 
pears  in  the  same  direction  from  all  parts  of  the  earth's  or- 
bit, though  190  millions  of  miles  in  diameter. 

838.  If  the  earth  had  only  a  diurnal  motion,  her  revolu- 
tion, in  respect  to  the  sun,  would  coincide  exactly  with  the 
same  revolution  in  respect  to  the  stars ;  but  while  she  is 
making  one  revolution  on  her  axis  towards  the  east,  she  ad- 
vances in  the  same  direction  about  one  degree  in  her  orbit, 
so  that  to  bring  the  same  meridian  towards  the  sun,  she 
must  make  a  little  more  than  one  entire  revolution. 
Fig.  213. 


How  is  the  difference  in  time  between  the  solar  and  siderial  year  ac- 
counted for  ?  The  earth's  orbit  is  but  a  point,  in  reference  to  a  star; 
how  is  this  illustrated  1 


TIME.  273 

To  make  this  plain,  suppose  the  sun,  5,  fig.  213,  to  be  ex- 
actly on  a  meridian  line  marked  at  e,  on  the  earth  A,  on  a 
given  day.  On  the  next  day,  the  earth,  instead  of  being  at 
A,  as  on  the  day  before,  advances  in  its  orbit  to  B,  and  in 
the  mean  time  having  completed  her  revolution,  in  respect 
to  a  star,  the  same  meridian  line  is  not  brought  under  the 
sun,  as  on  the  day  before,  but  falls  short  of  it,  as  at  e,  so  that 
the  earth  has  to  perform  more  than  a  revolution,  by  the  dis- 
tance from  e  to  o,  in  order  to  bring  the  same  meridian 
again  under  the  sun.  So  on  the  next  day,  when  the  earth 
is  at  C,  she  must  again  complete  more  than  two  revolutions, 
since  leaving  A,  by  the  space  from  e  to  o,  before  it  will  again 
be  noon  at  e. 

839.  Thus,  it  is  obvious,  that  the  earth  must  complete 
one  revolution,  and  a  portion  of  a  second  revolution,  equal 
to  the  space  she  has  advanced  in  her  orbit,  in  order  to  bring 
the  same  meridian  back  again  to  the  sun.     This  small  por- 
tion of  a  second  revolution  amounts  daily  to  the  365th  part 
of  her  circumference,  and  therefore,  at  the  end  of  the  year, 
to  one  entire  rotation,  and  hence  in  365  days,  the  earth 
actually  turns  on  her  axis  366  times.     Thus,  as  one  com- 
plete rotation  forms  a  siderial  day,  there  must,  in  the  year, 
oe  one  siderial,  more  than  there  are  solar  days,  one  rotation 
of  the  earth,  with  respect  to  the  sun,  being  lost,  by  the 
earth's  yearly  revolution.     The  same  loss  of  a  day  happens 
to  a  traveller,  who,  in  passing  round  the  earth  towards  the 
west,  reckons  his  time  by  the  rising  and  setting  of  the  sun. 
If  he  passes  round  towards  the  east,  he  will  gain  a  day  for 
the  same  reason. 

EQUATION  or  TIME. 

840.  As  the  motion  of  the  earth  about  its  axis  is  perfect- 
ly uniform,  the  siderial  days,  as  we  have  already  seen,  are 
exactly  of  the  same  length,  in  all  parts  of  the  year.     But 
as  the  orbit  of  the  earth,  or  the  apparent  path  of  the  sun,  is 
inclined  to  the  earth's  axis,  and  as  the  earth  moves  with  dif- 
ferent velocities  in  different  parts  of  its  orbit,  the  solar,  or 
natural  days,  are  sometimes  greater  and  sometimes  less  than 

Hid  the  earth  only  a  diurnal  revolution,  would  the  siderial  and  solar 
time  agreel  Show  by  fig.  213,  how  siderial  differs  from  solar  time? 
Why  does  not  the  earth  turn  the  same  meridian  to  the  sun  at  the  same 
time  every  day  1  How  many  times  does  the  earth  turn  on  her  axis  in  a 
year  1  Why  does  she  turn  more  times  than  there  are  days  in  the  year  1 
Why  are  the  solar  days  sometimes  greater,  and  sometimes  less,  than  24 
hours  1 


274  TIME. 

24  hours,  as  shown  by  an  accurate  clock.  The  consequence 
is,  that  a  true  sun  dial,  or  noon  mark,  and  a  true  time  piece, 
agree  with  each  other  only  a  few  times  in  a  year.  The 
difference  between  the  sun  dial  and  clock,  thus  -shown,  is 
called  the  equation  of  time. 

The  difference  between  the  sun  and  a  well  regulated 
clock,  thus  arises  from  two  causes,  the  inclination  of  the 
earth's  axis  to  the  ecliptic,  and  the  elliptical  form  of  the 
earth's  orbit. 

841.  That  the  earth  moves  in  an  ellipse,  and  that  its  mo- 
tion is  more  rapid  sometimes  than  at  others,  as  well  as  that 
the  earth's  axis  is  inclined  to  the  ecliptic,  have  already  been 
explained  and  illustrated.     It  remains,  therefore,  to  show 
how  these  two  combined  causes,  the  elliptical  form  of  the 
orbit,  and  the  inclination  of  the  axis,  produce  the  disagree- 
ment between  the  sun  and  clock.     In  this  explanation,  we 
must  consider  the  sun  as  moving  around  the  ecliptic,  while 
the  earth  revolves  on  her  axis. 

842.  Equal,  or  mean  time,  is  that  which  is  reckoned  by 
a  clock,  supposed  to  indicate  exactly  24  hours,  from   12 
o'clock  on  one  day,  to  12  o'clock  on  the  next  day.     Ap- 
parent time,  is  that  which  is  measured  by  the  apparent  mo- 
tion of  the  sun  in  the  heavens,  as  indicated  by  a  meridian 
line,  or  sun  dial. 

843.  Were  the  earth's  orbit  a  perfect  circle,  fig.  207,  and 
her  axis  perpendicular  to  the  plane  of  this  orbit,  the  days 
would  be  of  a  uniform  length,  and  there  would  be  no  dif- 
ference between  the  clock  and  the  sun ;  both  would  indicate 
12  o'clock  at  the  same  time,  on  every  day  in  the  year.    But 
on  account  of  the  inclination  of  the  earth's  axis  to  the 
ecliptic,  unequal  portions  of  the  sun's  apparent  path  through 
the  heavens  will  pass  any  meridian  in  equal  times.     This 
may  be  readily  explained  to  the  pupil,  by  means  of  an  arti- 
ficial globe;  but  perhaps  it  will  be  understood  by  the  follow- 
ing diagram. 

Let  A  N  B  S,  fig.  214,  be  the  concave  of  the  heavens,  in 
the  centre  of  which  is  the  earth.  Let  the  line  A  B,  be  the 
equator,  extending  through  the  earth  and  the  heavens,  and 
let  A,  a,  b,  C,  c,  and  d,  be  the  ecliptic,  or  the  apparent  path 

What  is  the  difference  between  the  time  of  a  sun  dial  and  a  clock 
called  1  What  are  the  causes  of  the  difference  between  the  sun  and 
clock?  In  explaining  equation  of  time,  what  motion  is  considered  a» 
belonging  to  the  sun,  and  what  motion  to  the  earth  7  What  is  equal,  or 
mean  time  7  What  is  apparent  time  7 


TIME 


275 


of  the  sun  through  the  heavens.     Also,  let  A,  1,  2,  3,  4,  5, 
oe  equal  distances  on  the  equator,  and  A,  a,  b,  C,  c,  and  dt 
equal  portions  of  the  ecliptic,  corresponding  with  A  1,  2,  3, 
4,  and  5.     Now  we  will  suppose,  that  there  are  two  suns, 
namely,  a  false,  and  a  real  one ;  that  the  false  one  passes 
through  the  celestial  equator,  which  is  only  an  extension  of 
the  earth's  equator 
to     the     heavens ; 
while  the  real  sun 
has  an  apparent  re- 
volution    through 
the   ecliptic  ;    and 
that  they  both  start 
from  the  point  A, 
at  the  same  instant. 
The   false    sun    is 
supposed    to    pass 
thro'  the   celestial 
equator  in  the  same 
time  that  the  real 
one  passes  through 
the  ecliptic,  but  not 
through  .the  same 
meridians    at    the 
same  time,  so  that  the  false  sun  arrives  at  the  points  1,  2,  3, 
4,  and  5,  at  the  time  when  the  real  sun  arrives  at  the  points 
&,  b,  C,  and  c.     When  the  two  suns  were  at  A,  the  starting 
point,  they  were  both  on  the  same  meridian,  but  when  the 
fictitious  sun  comes  to  1,  and  the  real  sun  to  a,  they  are  not 
in  the  same  meridian,  but  the  real  sun   is  westward  of  the 
fictitious  one,  the  real  sun  being  at  a  while  the  false  sun  is 
on  the  meridian  1,  consequently,  as  the  earth  turns  on  its 
axis  from  west  to  east,  any  particular  place  will  come  under 
the  sun's  real  meridian,  sooner  than  under  the  fictitious  sun's 
meridian  ;  that  is,  it  will  be  12  o'clock  by  the  true  sun,  be- 
fore it  is  12  o'clock  by  the  false  sun,  or  by  a  true  clock  ;  but 
were  the  true  sun  in  place  of  the  false  one,  the  sun  and 


In  fig.  214,  which  is  the  celestial  equator,  and  which  the  ecliptic  1 
Through  which  of  these  circles  does  the  false,  and  through  which  does 
the  true  sun  pass  1  When  the  real  sun  arrives  to  «,  and  the  false  one  to 
1,  are  they  both  on  the  same  meridian  1  Which  is  then  most  westward  T 
When  the  two  suns  are  at  1,  and  a,  why  will  any  meridian  come  first 
under  the  real  sun  1  Were  the  true  sun  in  place  of  the  false  one,  why 
would  the  sun  and  clock  agree  1 


276  TIME. 

clock  wbuld  agree.  While  the  true  sun  is  passing  through 
that  quarter  of  his  orbit,  from  a  to  C,  and  the  fictitious  sun 
from  1  to  3,  it  will  always  be  noon  by  the  true  sun  before  it 
is  noon  by  the  false  sun,  and  during  this  period,  the  sun  will 
be  faster  than  the  clock. 

When  the  true  sun  arrives  at  C,  and  the  false  one  at  3 
they  are  both  on  the  same  meridian,  and  the  sun  and  clock 
agree.  But  while  the  real  sun  is  passing  from  C  to  B,  and 
the  false  one  from  3  to  B,  any  meridian  comes  later  under 
the  true  sun  than  it  does  under  the  false,  arid  then  it  is 
noon  by  the  sun  after  it  is  noon  by  the  clock,  and  the  sun  is 
then  said  to  be  sloiver  than  the  clock.  At  B,  both  suns  are 
again  on  the  same  meridian,  and  then  again  the  sun  and 
clock  agree. 

We  have  thus  followed  the  real  sun  through  one  half  of 
his  true  apparent  place  in  the  heavens,  and  the  false  one 
through  half  the  celestial  equator,  and  have  seen  that  the 
two  suns,  since  leaving  the  point  A,  have  been  only  twice  on 
the  same  meridian  at  the  same  time.  It  has  been  supposed 
that  the  two  suns  passed  through  equal  arcs,  in  equal  times, 
the  real  sun  through  the  ecliptic,  and  the  false  one  through 
the  equator.  The  place  of  the  false  sun  may  be  considered 
as  representing  the  place  where  the  real  sun  would  be,  in 
case  the  earth's  axis  had  no  inclination,  and  consequently  it 
agrees  with  the  clock  every  24  hours.  But  the  true  sun,  as 
he  passes  round  in  the  ecliptic,  comes  to  the  same  meridian, 
sometimes  sooner,  and  sometimes  later,  and  in  passing  around 
the  other  half  of  the  ecliptic,  or  in  the  other  half  year,  the 
same  variations  succeed  each  other. 

The  two  suns  are  supposed  to  depart  from  the  point  A,  on 
the  20th  of  March,  at  which  time  the  sun  and  clock  coincide. 
From  this  time,  the  sun  is  faster  than  the  clock,  until  the  two 
suns  come  together  at  the  point  C,  which  is  on  the  21st  of 
June,  when  the  sun  and  clock  again  agree.  From  this  period 
the  sun  is  slower  than  the  clock,  until  the  23d  of  September, 
and  faster  again  until  the  21st  of  December,  at  which  time 
they  agree  as  before. 

We  have  thus  seen  how  the  inclination  of  the  earth's  axis, 
and  the  consequent  obliquity  of  the  equator  to  the  ecliptic, 

While  the  suns  are  passing1  from  A  to  C,  and  from  1  to  3,  will  the 
sun  be  faster  or  slower  than  the  clock  1  When  the  two  suns  are  at  C, 
and  3,  why  will  the  sun  and  clock  agree  1  While  the  real  sun  is  passing 
from  B  to  C,  which  is  fastest,  the  clock  or  sun  1  What  does  the  place 
of  the  false  sun  represent,  in  fig.  214  7 


TIME  277 

causes  the  sun  and  clock  to  disagree,  and  on  what  days  they 
would  coincide,  provided  nu  other  cause  interfered  with  their 
agreement.  But  although  the  inclination  of  the  earth's 
axis  would  bring  the  sun  and  clock  together  on  the  above- 
mentioned  days,  yet  this  agreement  is  counteracted  by  an- 
other cause,  which  is  the  elliptical  form  of  the  earth's  orbit, 
and  though  the  sun  and  clock  do  agree  four  times  in  the 
year,  it  is  not  on  any  of  the  days  above  mentioned. 

It  has  been  shown  by  fig.  204,  that  the  earth  moves  more 
rapidly  in  one  part  of  its  orbit  than  in  another.  When  it  is 
nearest  the  sun,  which  is  in  the  winter,  its  velocity  is  great- 
er than  when  it  is  most  remote  from  him,  as  in  the  summer. 
Were  the  earth's  orbit  a  perfect  circle,  the  sun  and  clock 
would  coincide  on  the  days  above  specified,  because  then  the 
only  disagreement  would  arise  from  the  inclination  of  the 
earth's  axis.  But  since  the  earth's  distance  from  the  sun  is 
constantly  changing,  her  rate  of  velocity  also  changes,  and 
she  passes  through  unequal  portions  of  her  orbit  in  equal 
times.  Hence,  on  some  days,  she  passes  through  a  greater 
portion  of  it  than  on  others,  and  thus  this  becomes  another 
cause  of  the  inequality  of  the  sun's  apparent  motion. 

The  elliptical  form  of  the  earth's  orbit  would  prevent  the 
coincidence  of  the  sun  and  clock  at  all  times,  except  when 
the  earth  is  at  the  greatest  distance  from  the  sun,  which 
happens  on  the  1st  of  July,  and  when  she  is  at  the  least  dis- 
tance from  him,  which  happens  on  the  1st  of  January.  As 
the  earth  moves  faster  in  the  winter  than  in  the  summer, 
from  this  cause,  the  sun  would  be  faster  than  the  clock  from 
the  1st  of  July  to  the  1st  of  January,  and  then  slower  than 
the  clock  from  the  1st  of  January  to  the  1st  of  July. 

844.  We  have  now  explained,  separately,  the  two  causes 
which  prevents  the  coincidence  of  the  sun  and  clock.  By  the 
first  cause,  which  is  the  inclination  of  the  earth's  axis,  they 
would  agree  four  times  in  the  year,  and  by  the  second  cause, 
the  irregularity  of  the  earth's  motion,  they  would  coincide 
only  twice  in  the  year. 

Now,  these  two  causes  counteract  the  effects  of  each 
other,  so  that  the  sun  and  clock  do  not  coincide  on  any  of  the 

The  inclination  of  the  earth's  axis  would  make  the  sun  and  clock 
agree  in  March,  and  the  other  months  above  named :  why  then  do  they 
not  actually  agree  at  those  times  1  Were  the  earth's  orbit  a  perfect  cir- 
cle, on  what  days  would  the  sun  and  clock  agree  7  How  does  the  form 
of  the  earth's  orbit  interfere  with  the  agreement  of  the  sun  ard  clock 
on  those  days  1  At  what  times  would  the  form  of  the  earth's  orbit 
bring  the  sun  and  clock  to  agree  1 

Ot 


278  PRECESSION  OP  EttUINOXES. 

days,  when  either  cause,  taken  singly,  would  make  an  agree- 
ment between  them.  The  sun  and  clock,  therefore,  are  to- 
gether, only  when  the  two  causes  balance  each  other ;  that 
is,  when  one  cause  so  counteracts  the  other,  as  to  make  a 
mutual  agreement  between  them.  This  effect  is  produced 
four  times  in  the  year;  namely,  on  the  15th  of  April,  15th 
of  June,  31st  of  August,  and  24th  of  December.  On  these 
days,  the  sun,  and  a  clock  keeping  exact  time,  coincide,  and 
on  no  others.  The  greatest  difference  between  the  sun  and 
clock,  or  between  the  apparent  and  mean  time,  is  16£  min- 
utes, which  takes  place  about  the  1st  of  November.' 

PRECESSION  OF  THE  EQUINOXES. 

845.  A  tropical  year  is  the  time  it  takes  the  sun  to  pass 
from  one  equinox,  or  tropic,  to  the  same  tropic,  or  equinox, 
again. 

846.  A  siderial  year  is  the  time  it  takes  the  sun  to  per- 
form his  apparent  annual  revolution,  from  a  fixed  star,  to 
the  same  fixed  star  again. 

Now  it  has  been  found  that  these  two  complete  revolu- 
tions are  not  finished  in  exactly  the  same  time,  but  that  it 
takes  the  sun  about  20  minutes  longer  to  complete  his  ap- 
parent revolution  in  respect  to  the  star,  than  it  does  in  re- 
spect to  the  equinox,  and  hence  the  siderial  year  is  about  20 
minutes  longer  than  the  tropical  year.  The  revolution  of 
the  earth  from  equinox  to  equinox,  again,  therefore,  precedes 
its  complete  revolution  in  the  ecliptic  by  about  20  minutes, 
for  the  absolute  revolution  of  the  earth  is  measured  by  its 
return  to  the  fixed  star,  and  not  by  the  return  of  the  sun  to 
the  same  equinoctial  point.  This  apparent  falling  back  of 
the  equinoctial  point,  so  as  to  make  the  time  when  it  meets 
the  sun  precede  the  time  when  the  earth  makes  its  complete 
revolution  in  respect  to  the  star,  is  called  the  precession  of 
the  equinoxes. 

The  distance  which  the  sun  thus  gains  upon  the  fixed 
star,  or  the  difference  between  the  sun  and  star,  when  the 

The  inclination  of  the  earth's  axis  would  make  the  sun  and  clock 
agree  four  times  in  the  year,  and  the  form  of  the  earth's  orbit  would 
make  them  agree  twice  in  the  year ;  now  show  the  reason  why  they  do 
not  a<*ree  from  these  causes,  on  the  above  mentioned  days,  and  why 
they  do  agree  on  other  days.  On  what  days  do  the  sun  and  clock 
agreed  What  is  a  tropical  year  1  What  is  a  siderial  year!  What  is 
the  difference  in  the  time  which  it  takes  the  sun  to  complete  his  revolu- 
tion in  respect  to  a  star,  and  in  respect  to  the  equinox?  Explain  what 
is  meant  by  the  precession  of  the  equinoxes. 


PRECESSION  OF  EQ.UINOXES,  279 

sun  has  arrived  at  the  equinoctial  point,  amounts  to  50  sec- 
onds of  a  degree,  thus  making  the  equinoctial  point  recede 
50  seconds  of  a  degree,  (when  measured  by  the  signs  of  the 
zodiac,)  westward,  every  year,  contrary  to  the  sun's  annual 
progressive  motion  in  the  ecliptic. 
Fig.  215. 


To  illustrate  this  hy  a  figure,  suppose  S,  fig.  215,  to  be 
the  sun,  E  the  earth,  and  o  a  fixed  star,  all  in  a  straight  line 
with  respect  to  each  other.  Let  it  be  supposed  that  this  op- 
position takes  place  on  the  21st  of  March,  at  the  vernal  equi- 
nox, and  that  at  that  time  the  earth  is  exactly  between  the 
sun  and  the  star.  Now  when  the  earth  has  performed  a 
complete  revolution  around  its  orbit  b,  a,  as  measured  by  the 
star,  she  will  arrive  at  precisely  the  same  point  where  she 
now  is.  But  it  is  found  that  when  the  earth  comes  to  the 
same  equinoctial  point,  the  next  year,  she  has  not  gone  her 
complete  revolution  in  respect  to  the  star ;  the  equinoctial 
point  having  fallen  back  with  respect  to  the  star,  during  the 
year,  from  E  to  e,  so  that  the  earth,  after  having  completed 
her  revolution,  in  respect  to  the  equinox,  has  yet  to  pass  the 
space  from  e  to  E,  to  complete  her  revolution  in  respect  to 
the  star. 

The  space  from  E  to  e,  being  50  seconds  of  a  degree,  and 
the  equinoctial  point  falling  this  space  every  year  short  of 
the  place  where  the  sun  and  this  point  agreed  the  year  be- 
fore, it  is  obvious,  that  on  the  next  revolution  of  the  earth, 

How  many  seconds  of  a  degree  does  the  equinox  recede  every  year, 
when  the  sun's  place  is  compared  with  a  star  1  How  does  fig.  215  il- 
lustrate the  precession  of  the  equinoxes  1  Explain  fig.  215,  and  show 
from  what  points  the  equinoxes  fall  back  from  year  to  year. 


280  PRECESSION  OF  EQUINOXES. 

the  equinox  will  not  be  found  at  et  but  at  z,  so  that  the  earth, 
having  completed  her  second  revolution  in  respect  to  the 
sun  when  at  i,  will  still  have  to  pass  from  i  to  JE,  before  she 
completes  another  revolution  in  respect  to  the  star. 

847.  The  precession  of  the  equinoxes,  being  50  seconds 
of  a  degree,  every  year,  contrary  to  the  sun's  apparent  mo- 
tion, or  about  20  minutes,  in  time,  short  of  the  point  where 
the  sun  and  equinoxes  coincided  the  year  before,  it  follows, 
that  the  fixed  stars,  or  those  in  the  sign  of  the  zodiac,  move 
forward  every  year  50  seconds,  with  respect  to  the  equi- 
noxes. 

In  consequence  of  this  precession,  in  2160  years,  those 
stars  which  now  appear  in  the  beginning  of  the  sign  Aries, 
for  instance,  will  then  appear  in  the  beginning  of  Taurus, 
having  moved  forward  one  whole  sign,  or  30  degrees,  with 
respect  to  the  equinoxes,  or  the  equinoxes  having  gone 
backwards  30  degrees,  with  respect  to  the  stars.  In  12,960 
years,  or  6  times  2160  years,  therefore,  the  stars  will  appear 
to  have  moved  forward  one  half  of  the  whole  circle  of  the 
heavens,  so  that  those  which  now  appear  in  the  first  degree 
of  the  sign  Aries,  will  then  be  in  the  opposite  point  of  the 
zodiac,  and,  therefore,  in  the  first  degree  of  Libra.  And  in 
12,600  years  more,  because  the  equinoxes  will  have  fallen 
back  the  other  half  of  the  circle,  the  stars  will  appear  to 
have  gone  forward  from  Libra  to  Aries,  thus  completing  the 
whole  circle  of  the  zodiac. 

Thus,  in  about  26,000  years,  the  equinox  will  have  gone 
backwards  a  whole  revolution  around  the.  axis  of  the  eclip- 
tic, and  the  stars  will  appear  to  have  gone  forward  the  whole 
circle  of  the  zodiac. 

848.  The  discovery  of  the  precession  of  the  equinoxes 
has  thrown  much  light  on  ancient  astronomy  and  chronolo- 
gy, by  showing  an  agreement  between  ancient  and  modern 
observations,  concerning  the  places  of  the  signs  of  the  zo- 
diac, not  to  be  reconciled  in  any  other  manner. 

A  complete  explanation  of  the  cause  which  occasions  the 
precession  of  the  equinoxes,  would  require  the  aid  of  the 
most  abstruse  mathematics,  and  therefore  cannot  be  properly 

How  many  minutes,  in  time,  is  the  precession  of  the  equinoxes  per 
year '?  What  effect  does  this  precession  produce  on  the  fixed  stars  1 
How  many  years  is  a  star  in  going  forward  one  degree,  in  respect  to  the 
equinoxes  1  In  how  many  years*will  the  stars  appear  to  have  passed 
half  around  the  heavens'?  In  what  period  will  the  earth  appear  to 
have  gone  backwards  one  whole  revolution  1  In  what  respect  is  the 
precession  of  the  equinoxes  an  important  subject  7 


MOON.  281 

introduced  here.     The  cause  itself  may,  however,  be  stated 
in  a  few  words. 

849.  It  has  already  been  explained,  that  the  revolution  of 
the  earth  round  its  axis,  has  caused  an  excess  of  matter  to 
be  accumulated  at  the  equator,  and  hence,  that  the  equatorial 
is  greater  than  the  polar  diameter,  by  34  miles.     Now  the 
attraction  of  the  sun  and  moon,  on  this  accumulated  matter 
at  the  equator,  has  the  effect  of  slowly  turning  the  earth  about 
the  axis  .of  the  ecliptic,  and  thus  causing  the  precession  of 
the  equinoxes, 

THE  MOON. 

850.  While  the  earth  revolves  round  the  sun,  the  moon 
revolves  round  the  earth,  completing  her  revolution  once  in 
27  days,  7  hours,  and  43  minutes,  and  at  the  distance  of 
240,000  miles  from  the  earth.     The  period  of  the  moon's 
change,  that  is,  from  new  moon  to  new  moon  again,  is  29 
days,  12  hours,  and  44  minutes. 

851.  The  time  of  the  moon's  revolution  round  the  earth 
is  called  her  periodical  month ;  and  the  time  from  change 
to  change  is  called  her  si/nodical  month.     If  the  earth  had 
no  annual  motion,  these  two  periods  would  be  equal,  but 
because  the  earth  goes  forward  in  her  orbit,  while  the  moon 
goes  round  the  earth,  the  moon  must  go  as  much  farther, 
from  change  to  change,  to  make  these  periods  equal,  as  the 
earth  goes  forward  during  that  time,  which  is  more  than  the 
twelfth  part  of  her  orbit,  there  being  more  than  twelve  lunar 
periods  in  the  year. 

852.  These  two  revolutions  may  be  familiarly  illustrated 
by  the  motions  of  the  hour  and  minute  hands  of  a  watch. 
Let  us  suppose  the  12  hours  marked  on  the  dial  plate  of  a 
watch  to  represent  the  12  signs  of  the  zodiac  through  which 
the  sun  seems  to  pass  in  his  yearly  revolution,  while  the 
hour  hand  of  the  watch  represents  the  sun,  and  the  minute 
hand  the  moon.     Then,  as  the  hour  hand  goes  around  the 
dial  plate  once  in   12  hours,  so  the  sun  apparently  goes 
around  the  zodiac  once  in  12  months;  and  as  the  minute 
hand  makes  12  revolutions  to  one  of  the  hour  hand,  so  the 
moon  makes  12  revolutions  to  one  of  the  sun.     But  the 

What  is  the  cause  of  the  precession  of  the  equinoxes  1  What  is  the 
period  of  the  moon's  revolution  round  the  earth  1  What  is  the  period 
from  new  moon  to  new  moon  again  1  What  are  these  two  periods 
called  1  Why  are  not  the  periodical  and  synodical  months  equal  1 
How  are  these  two  revolutions  of  the  moon  illustrated  by  the  two 
hands  of  a  watch  1 

24* 


282  MOON. 

moon,  or  minute  hand,  must  go  more  than  once  round,  from 
any  point  on  the  circle,  where  it  last  came  in  conjunction 
with  the  sun,  or  hour  hand,  to  overtake  it  again,  since  the 
hour  hand  will  have  moved  forward  of  the  place  where  it 
was  last  overtaken,  and  consequently  the  next  conjunction 
must  be  forward  of  the  place  where  the  last  happened. 
During  an  hour,  the  hour  hand  describes  the  twelfth  part  of 
the  circle,  but  the  minute  hand  has  not  only  to  go  round  the 
whole  circle  in  an  hour,  but  also  such  a  portion  of  it,  as  the 
hour  hand  has  moved  forward  since  they  last  met.  Thus, 
at  12  o'clock,  the  hands  are  in  conjunction;  the  next  con 
junction  is  5  minutes  27  seconds  past  I  o'clock  j  the  next, 
10  min.  54  sec.  past  II  o'clock:  the  third,  16  min.  21  sec. 
past  III;  the  4th,  21  min.  49  sec.  past  IV;  the  5th,  27  min. 
10  sec.  past  V;  the  6th,  32  min.  43  sec.  past  VI;  the  7th, 
38  min.  10  sec.  past  VII ;  the  8th,  43  min.  38  sec.  part  VIII ; 
the  9th,  49  min.  5  sec.  past  IX;  the  10th,  54  min.  32  sec. 
past  X ;  and  the  next  conjunction  is  at  XII. 

853.  Now  although  the  moon  passes  around  the  earth  in 
27  days  7  hours  and  43  minutes,  yet  her  change  does  not 
take  place  at  the  end  of  this  period,  because  her  changes 
are  not  occasioned  by  her  revolutions  alone.,  but  by  her 
coming  periodically  into  the  same  position  in  respect  to  the 
sun.  At  her  change,  she  is  in  conjunction  with  the  sun, 
when  she  is  not  seen  at  all,  and  at  this  time  astronomers  call 
it  new  moon,  though  generally,  we  say  it  is  new  moon  two 
days  afterwards,  when  a  small  part  of  her  face  is  to  be 
seen.  The  reason  why  there  is  not  a  new  moon  at  the  end 
of  27  days,  will  be  obvious,  from  the  motions  of  the  hands 
of  a  watch  :  for  we  see  that  more  than  a  revolution  of  the 
minute  hand  is  required  to  bring  it  again  in  the  same 
position  with  the  hour  hand,  by  about  the  twelfth  part  of 
the  circle. 

The  same  principle  is  true  in  respect  to  the  moon;  for  as 
the  earth  advances  in  its  orbit,  it  takes  the  moon  2  days  5 
hours  and  I  minute  longer  to  come  again  in  conjunction 
with  the  sun,  than  it  does  to  make  her  monthly  revolution 
round  the  earth ;  and  this  2  days  5  hours  and  1  minute 

Mention  the  time  of  several  conjunctions  between  the  two  hands  of  a 
watch  ?  Why  do  not  the  moon's  changes  take  place  at  the  periods  of 
her  revolution  around  the  earth  1  How  much  longer  does  it  take  the 
moon  to  come  again  in  conjunction  with  the  sun,  than  it  does  to  perform 
her  periodical  revolution  ?  How  is  it  proved  that  the  moon  makes  hut 
one  revolution  on  her  axis,  as  she  passes  around  the  earth  "* 


MOON.  283 

oemg  added  to  27  days  7  hours  and  43  minutes,  the  time  of 
the  periodical  revolution  makes  29  days  12  hours  and  44 
minutes,  the  period  of  her  synodical  revolution. 

854.  The  moon  always  presents  the  same  side,  or  face, 
towards  the  earth,  and  hence  it  is  evident  that  she  turns  on 
ner  axis  but  once,  while  she  is  performing  one  revolution 
round  the  earth,  so  that  the  inhabitants  of  the  moon  have  but 
one  day,  and  one  night,  in  the  course  of  a  lunar  month. 

One  half  of  the  moon  is  never  in  the  dark,  because  when 
this  half  is  not  enlightened  by  the  sun,  a  strong  light  is  re- 
flected to  her  from  the  earth,  during  the  sun's  absence.  The 
other  half  of  the  moon  enjoys  alternately  two  weeks  of  the 
rfun's  light,  and  two  weeks  of  total  darkness. 

855.  The  moon  is  a  globe,  like  our  earth,  and,  like  the 
earth,  shines  only  by  the   light   reflected   from  the   sun ; 
therefore,  while  that  half  of  her  which  is  turned  towards  the 
sun  is  enlightened,  the  other  half  is  in  darkness.    Did  the 
moon  shine  by  her  own  light,  she  would  be  constantly  visible 
10  us,  for  then,  being  an  orb,  and  every  part  illuminated,  we 
should  see  her  constantly  full  and  round,  as  we  do  the  sun. 

856.  One  of  the  most  interesting  circumstances  to  us,  res- 
pecting the  moon,  is,  the  constant  changes  which  she  un- 
dergoes, in  her  passage  around  the  earth.     When  she  first 
appears,  a  day  or  two  after  her  change,  we  can  see  only  a 
small  portion  of  her  enlightened  side,  which  is  in  the  form 
of  a  crescent ;  and  at  this  time  she  is  commonly  called  new 
moon.     From  this  period,  she  goes  on  increasing,  or  show- 
ing more  and  more  of  her  face  every  evening,  until  at  last 
she  becomes  round,  and  her  face  fully  illuminated.     She 
then  begins  again  to  decrease,  by  apparently  losing  a  small 
section  of  her  face,  and  the  next  evening  another  small  sec- 
tion from  the  same  part,  and  so  on,  decreasing  a  little  every 
day,  until  she  entirely  disappears  ;  and  having  been  absent 
a  day  or  two,  re-appears,  in  the  form  of  a  crescent,  or 
new  moon,  as  before. 

857.  When  the  moon  disappears,  she  is  said  to  be  in  con- 
junction, that  is,  she  is  in  the  same  direction  from  us  with 
the  sun.     When  she  is  full,  she  is  said  to  be  in  opposition, 
that  is,  she  is  in  that  part  of  the  heavens  opposite  to  the  sun, 
as  seen  by  us. 

One  half  of  the  moon  is  never  in  the  dark;  explain  why  this  is  so  1 
How  long  is  the  day  and  night  at  the  other  half?  How  is  it  shown 
that  the  moon  shines  only  by  reflected  light  ?  When  is  the  moon  said 
lo  be  in  conjunction  with  the  sun,  and  when  in  opposition  to  the  sun  ? 


284  MOON 

858.  The  different  appearances  of  the  moon,  from  new  to 
full,  and  from  full  to  change,  are  owing  to  her  presenting 
different  portions  of  her  enlightened  surface  towards  us  at 
different  times.  These  appearances  are  called  the  phases  of 
the  moon,  and  are  easily  accounted  for,  and  understood,  by 
the  following  figure. 

Fig.  216. 


d, 


Let  S,  fig.  216,  be  the  sun,  JE  the  earth,  and  A,  B,  C,  1), 

E,  the  moon  in  different  parts  of  her  orbit.  Now  when  the 
moon  changes,  or  is  in  conjunction  with  the  sun,  as  at  A, 
her  dark  side  is  turned  towards  the  earth,  and  she  is  invisi- 
ble, as  represented  at  a.  The  sun  always  shines  on  one 
half  of  the  moon,  in  every  direction,  as  represented  at  A 
and  B,  on  the  inner  circle  ;  but  we  at  the  earth  can  see  only 
such  portions  of  the  enlightened  half  as  are  turned  towards 
us.  After  her  change,  when  she  has  moved  from  A  to  JB,  a 
small  part  of  her  illuminated  side  'omes  in  sight,  and  she 
appears  horned,  as  at  b,  and  is  then  called  the  new  moon. 
When  she  arrives  at  C,  several  days  afterwards,  one  half 
of  her  disc  is  visible,  and  she  appears  as  at  c,  her  appearance 
being  the  same  in  both  circles.  At  this  point  she  is  said  to 
be  in  her  first  quarter,  because  she  has  passed  through  a 
quarter  of  her  orbit,  and  is  90  degrees  from  the  place  of  her 
conjunction  with  the  sun.  At  D,  she  shows  us  still  more 
of  her  enlightened  side,  and  is  then  said  to  appear  gibbous, 

What  are  the  phases  of  the  moon  7  Describe  fig.  216,  and  show 
how  the  moon  passes  from  change  to  full,  and  from  full  to  change  ? 
What  is  said  concerning  the  phases  of  the  earth,  as  seen  from  the 
moon  7 


MOON.  285 

as  at  d.  When  she  comes  to  JE,  her  whole  enlightened  side 
is  turned  towards  the  earth,  and  she  appears  in  all  the 
splendour  of  a  full  moon.  During-  the  other  half  of  her 
revolution,  she  daily  shows  less  and  less  of  her  illuminated 
side,  until  she  again  becomes  invisible  by  her  conjunction 
with  the  sun.  Thus,  in  passing  from  her  conjunction  a,  to 
her  full,  e,  the  moon  appears  every  day  to  increase,  while  in 
going  from  her  full  to  her  conjunction  again,  she  appears  to 
us  constantly  to  decrease,  but  as  seen  from  the  sun,  she  ap- 
pears always  full. 

859.  How  the  Earth  appears  at  the  Moon. — The  earth, 
seen   by  the  inhabitants  of  the  moon,  exhibits  the  same 
phases  that  the  moon  does  to  us,  but  in  a  contrary  order. 
When  the  moon  is  in  her  conjunction,  and  consequently 
invisible  to  us,  the  earth  appears  full  to  the  people  of  the 
moon,  and  when  the  moon  is  full  to  us,  the  earth  is  dark  to 
them. 

The  earth  appears  thirteen  times  larger  to  the  lunarians 
than  the  moon  does  to  us.  As  the  moon  always  keeps  the 
same  side  towards  the  earth,  and  turns  on  her  axis  only  as 
she  moves  round  the  earth,  we  never  see  her  opposite  side. 
Consequently,  the  lunarians  who  live  on  the  opposite  side 
to  us  never  see  the  earth  at  all.  To  those  who  live  on  the 
middle  of  the  side  next  to  us,  our  earth  is  always  visible, 
and  directly  over  head,  turning  on  its  axis  nearly  thirty 
times  as  rapidly  as  the  moon,  for  she  turns  only  once  in 
about  thirty  days.  A  lunar  astronomer,  who  should  happen 
to  live  directly  opposite  to  that  side  of  the  moon,  which  in 
next  to  us,  would  have  to  travel  a  quarter  of  the  circum- 
ference of  the  moon,  or  about  1500  miles,  to  see  our  earth 
above  the  horizon,  and  if  he  had  the  curiosity  to  see  such  a 
glorious  orb,  in  its  full  splendour  over  his  head,  he  must 
travel  3000  miles.  But  if  his  curiosity  equalled  that  of 
the  terrestrials,  he  would  be  amply  compensated  by  behold- 
ing so  glorious  a  nocturnal  luminary,  a  moon  thirteen  times 
as  large  as  ours. 

860.  That  the  earth  shines  upon  the  moon  as  the  moon 
does  upon  us,  is  proved  by  the  fact  that  the  outline  of  her 
whole  disc  may  be  seen,  when  only  a  part  of  it  is  enlighten- 
ed by  the  sun.     Thus  when  the  sky  is  clear,  and  the  moon 

Wnen  does  the  earth  appear  full  at  the  moon  1  When  is  the  earth  in 
Iier  change,  to  the  people  of  the  moon  7  Why  do  those  who  live  on  one 
side  of  the  moon  never  see  the  earth'?  How  is  it  known  that  the  earth 
shines  upon  the  moon,  as  the  moon  does  upon  us  1 


286  MOON. 

only  two  or  three  days  old,  it  is  not  uncommon  to  see  ifie 
brilliant  new  moon,  with  her  horns  enlightened  by  the  sun, 
and  at  the  same  time,  the  old  moon  faintly  illuminated  by 
reflection  from  the  earth.  This  phenomenon  is  sometimes 
called  "  the  old  moon  in  the  new  moon's  arms." 

It  was  a  disputed  point  among  former  astronomers,  whether 
the  moon  has  an  atmosphere ;  but  the  more  recent  discoveries 
have  decided  that  she  has  an  atmosphere,  though  there  is 
reason  to  believe  that  it  is  much  less  dense  than  ours. 

861.  Surface  of  the  Moon. — When  the  moon's  surface  is 
examined  through  a  telescope,  it  is  found  to  be  wonderfully 
diversified,  for  besides  the  dark  spots  perceptible  to  the  naked 
eye,  there  are  seen  extensive  valleys,  and  long  ridges  of 
highly  elevated  mountains. 

862.  Some  of  these  mountains,  according  to  Dr.  Herschel, 
are  4  miles  high,  while  hollows  more  than  3  mile?  deep, 
and  almost  exactly  circular,  appear  excavated  on  the  plains. 
Astronomers  have  been  at  vast  labour  to  enumerate,  figure, 
and  describe,  the  mountains  and  spots  on  the  surface  of  the 
moon,  so  that  the  latitude  and  longitude  of  about  100  spots 
have  been  ascertained,  and  their  names,  shapes,  and  relative 
positions  given.     A  still  greater  number  of  mountains  have 
been  named,  and  their  heights  and  the  length  of  their  bases 
detailed. 

863.  The  deep  caverns,  and  broken  appearance  of  the 
moon's  surface,  long  since  induced  astronomers,  to  believe 
that  such  effects  were  produced  by  volcanoes,  and  more  re- 
cent discoveries  have  seemed  to  prove  that  this  suggestion 
was  not  without  foundation.     Dr.  Herschel  saw  with  his 
telescope,  what  appeared  to  him  three  volcanoes  in  the  moon, 
two  of  which  were  nearly  extinct,  but  the  third  was  in  the 
actual  state  of  eruption,  throwing  out  fire,  or  other  luminous 
matter,  in  vast  quantities. 

864.  It  was  formerly  believed  that  several  large  spots, 
which  appeared  to  have  plane  surfaces,  were  seas,  or  lakes, 
and  that  a  part  of  the  moon's  surface  was  covered  with 
water,  like  that  of  our  earth.     But  it  has  been  found,  on 
closely  observing  these  spots,  when  they  were  in  such  a 
position  as  to  reflect  the  sun's  light  to  the  earth,  had  they 
been  water,  that  no  such  reflection  took  place.     It  has  also 


What  is  said  concerning  the  moon's  atmosphere*?  How  high  ar* 
some  of  the  mountains,  and  how  deep  the  caverns  of  the  moon'?  What 
is  said  concerning  the  volcanoes  of  the  moon'? 


ECLIPSES.  287 

been  found,  that  when  these  spots  were  turned  in  a  certain 
position,  their  surfaces  appeared  rough,  and  uneven ;  a 
certain  indication  that  they  are  not  water.  These  circum- 
stances, together  with  the  fact,  that  the  moon's  surface  is 
never  obscured  hy  mist  or  vapor,  arising  from  the  evaporation 
of  water  from  her  surface,  have  induced  astronomers  to  be- 
lieve, that  the  moon  has  neither  seas,  lakes,  nor  rivers,  and 
indeed  that  no  water  exists  there. 

ECLIPSES. 

865.  Every  planet  and  satellite  in  the  solar  system  is  il- 
luminated by  the  sun,  and  hence  they  cast  shadows  in  the 
direction  opposite  to  him,  just  as  the  shadow  of  a  man 
reaches  from  the  sun.     A  shadow  is  nothing  more  than  the 
interception  of  the  rays  of  light  by  an  opaque  body.     The 
earth  always  makes  a  shadow,  which  reaches  to  an  immense 
distance  into  open  space,  in  the  direction  opposite  to  the  sun. 
When  the  earth,  turning  on  its  axis,  carries  us  out  of  the 
sphere  of  the  sun's  light,  we  say  it  is  sunset,  and  then  we 
pass  into  the  earth's  shadow,  and  night  comes  on.     When 
the  earth  turns  half  round  from  this  point,  and  we  again 
emerge  out  of  the  earth's  shadow,  we  say,  the  sun  rises,  and 
then  day  begins. 

866.  Now  an  eclipse  of  the  moon  is  nothing  more  than 
her  falling  into  the  shadow  of  the  earth.     The  moon,  hav- 
ing no  light  of  her  own,  is  thus  darkened,  and  we  say  she  is 
eclipsed.     The  shadow  of  the  moon  also  reaches  to  a  great 
distance  from  her.    We  know  that  it  reaches  at  least  240,000 
miles,  because  it  sometimes  reaches  the  earth.     An  eclipse 
of  the  sun  is  occasioned  whenever  the  earth  falls  into  the 
shadow  of  the  moon.     Hence,  in  eclipses,  whether  of  the 
sun  or  noon,  the  two  planets  and  the  sun  must  b?  nearly  in 
a  straight  line  with  respect  to  each  other.    In  eclipses  of  the 
moon,  the  earth  is  between  the  sun  and  moon,  and  in  eclipses 
of  the  sun,  the  moon  is  between  the  earth  and  sun. 

867.  If  the  moon  went  around  the  sun  in  the  same  plane 
with  the  earth,  that  is,  were  the  moon's  orbit  on  the  plane 

What  is  supposed  concerning  the  lakes  and  seas  of  the  moon1?  On 
what  grounds  is  it  supposed  that  there  is  no  water  at  the  moon  1  What 
is  a  shadow  1  When  do  we  say  it  is  sunset,  and  when  do  we  say  it 
is  sunrise  1  What  occasions  an  eclipse  of  the  moon'?  What  causes 
eclipses  of  the  sun  1  In  eclipses  of  the  moon,  what  planet  is  between 
the  sun  and  moon!  In  eclipses  of  the  sun,  what  planet  is  between  the 
sun  and  earth  7  Why  is  there  not  an  eclipse  of  the  sun  at  every  con- 
junction of  the  sun  and  moon  1 


288  ECLIPSES. 

of  ihe  ecliptic,  there  would  happen  an  eclipse  of  the  sun  at 
every  conjunction  of  the  sun  and  moon,  or  at  the  time  of 
every  new  moon.  But  at  these  conjunctions  the  moon  doea 
not  come  exactly  between  the  earth  and  sun,  because  the  or- 
bit of  the  moon  is  inclined  to  the  ecliptic  at  an  angle  of  5^ 
degrees.  Did  the  planes  of  the  xorbits  of  the  earth  and 
moon  coincide,  there  would  be  an  eclipse  of  the  moon  at 
every  full,  for  then  the  moon  would  pass  exactly  through 
the  earth's  shadow. 

868.  One  half  of  the  moon's  orbit  being  elevated  5£  de- 
grees above  the  ecliptic,  the  other  half  is  depressed  as  much 
below  it,  and  thus  the  moon's  orbit  crosses  that  of  the  earth 
in  two  opposite  points,  called  the  moon's  nodes. 

As  the  nodes  of  the  moon  are  the  points  where  she  crosses 
the  ecliptic,  she  must  be  half  the  time  above,  and  the  other 
half  below  these  points.  The  node  in  which  she  crosses 
the  plane  of  the  ecliptic  upward,  or  towards  the  north,  is 
called  her  Ascending  node.  That  in  which  she  crosses  the 
same  plane  downward,  or  towards  the  south,  is  called  her 
descending  node. 

The  moon's  orbit,  like  those  of  the  other  planets,  is  ellip- 
tical, so  that  she  is  sometimes  nearer  the  earth  than  at  others. 
When  she  is  in  that  part  of  her  orbit,  at  the  greatest  dis- 
tance from  the  earth,  she  is  said  to  be  in  her  apogee,  and 
when  at  her  least  distance  from  the  earth,  she  is  in  her 
perigee. 

869.  Eclipses  can  only  happen  at  the  time  when  the  moon 
is  at,  or  near,  one  of  her  nodes,  for  at  no  other  time  is  she 
near  the  plane  of  the  earth's  orbit ;  and  since  the  earth  is 
always  in  this  plane,  the  moon  must  be  at,  or  near  it,  also, 
in  order  to  bring  the  two  planets  and  the  sun  in  the  same 
right  line,  without  which  no  eclipse  can  happen. 

870.  The  reason  why  eclipses  do  not  happen  oftener,  and 
at  regular  periods,  is  because  a  node  of  the  moon  is  usually 
only  twice,  and  never  more  than  three  times  in  the  year, 
presented  towards  the  sun.     The  average  number  of  total 
eclipses  of  both  luminaries,  in  a  century,  is  about  thirty,  and 
the  average  number  of  total  and  partial,  in  a  year,  about 

How  many  degrees  is  the  moon's  orbit  inclined  to  that  of  the 
earth  1  What  are  the  nodes  of  the  moon  1  What  is  meant  by  tha 
ascending  and  descending  nodes  of  the  moon  1  What  is  the  moon's, 
apogee,  and  what  her  perigee  1  Why  must  the  moon  be  at,  or  near, 
one  of  her  nodes,  to  occasion  an  eclipse  7  Why  do  not  eclipses  hap- 
oen  ofteo,  and  at  regular  periods  1 


ECLIPSES.  289 

four.  There  may  be  seven  eclipses  in  a  year,  including 
those  of  both  luminaries,  and  there  may  be  only  two.  When 
there  are  only  two,  they  are  both  of  the  sun. 

When  the  moon  is  within  16^  degrees  of  her  node,  at  the 
time  of  her  change,  she  is  so  near  the  ecliptic,  that  the  sun 
may  be  more  or  less  eclipsed,  and  when  she  is  within  12  de- 
grees of  her  node,  at  the  time  of  her  full,  the  moon  will  be 
more  or  less  eclipsed. 

871.  But  the  moon  is  more  frequently  within  16£  de- 
grees of  her  node  at  the  time  of  her  change,  than  she  is  within 
12  degrees  at  the  time  of  her  full,  and  consequently  there 
will  be  a  greater  number  of  solar,  than  of  lunar  eclipses,  in 
a  course  of  years.     Yet  more  lunar  eclipses  will  be  visible, 
at  any  one  place  on  the  earth,  than  solar,  because  the  sun,  be- 
ing so  much  larger  than  the  earth,  or  moon,  the  shadow  of 
these  oodies  must  terminate  in  a  point,  and  this  point  of  the 
moon's  shadow  never  covers  but  a  small  portion  of  the  earth's 
surface,  while  lunar  eclipses  are  visible  over  a  whole  hemi- 
sphere, and  as  the  earth  turns  on  its  axis,  are  therefore  visible 
to  more  than  half  the  earth.     This  will  be  obvious  by  figs. 
217  and  218,  where  it  will  be  observed  that  an  eclipse  of  the 
moon  may  be  seen  wherever  the  moon  is  visible,  while  an 
eclipse  of  the  sun  will  be  total  only  to  those  who  live  within 
the  space  covered  by  the  moon's  dark  shadow. 

872.  LUNAR  ECLIPSES. — When  the  moon  falls  into  the 
shadow  of  the  earth,  the  rays  of  the  sun  are  intercepted,  or 
hid  from  her,  and  she  then  becomes  eclipsed.     When  the 
earth's  shadow  covers  only  a  part  of  her  face,  as  seen  by  us, 
she  suffers  only  a  partial  eclipse,  one  part  of  her  disc  being 
obscured,  while  the  other  part  reflects  the  sun's  light.     But 
when  her  whole  surface  is  obscured  by  the  earth's  shadow, 
she  then  suffers  a  total  eclipse,  and  of  a  duration  proportion- 
ate to  the  distance  she  passes  through  the  earth's  shadow. 

Fig.  217  represents  a  total  lunar  eclipse;  the  moon  being 
in  the  midst  of  the  earth's  shadow.  Now  it  will  be  apparent 
that  in  the  situation  of  the  sun,  earth,  and  moon,  as  repre- 
sented in  the  figure,  this  eclipse  will  be  visible  from  all  parts 
of  that  hemisphere  of  the  earth  which  is  next  the  moon,  and 
that  the  moon's  disc  will  be  equally  obscured,  from  whatever 
point  it  is  seen.  When  the  moon  passes  through  only  a  part 

What  is  the  greatest,  and  what  the  least  number  of  eclipses,  that  can 
happen  in  a  year  1  Why  will  there  be  more  solar  than  lunar  eclipses  in 
the  course  of  years  *?  Why  will  more  lunar  than  solar  eclipses  be  visi- 
ble at  any  one  place  1 

25 


390 


ECLIPSES. 


of  the  earth's  shadow,  then  she  suffers  only  a  partial  eclipse, 
but  this  is  also  visible  from  the  whole  hemisphere  next  the 

Fig.  217. 
Eclipse  of  the,  Maori 


moon.  It  will  be  remembered  that  lunar  eclipses  happen 
only  at  full  moon,  the  sun  and  moon  being  in  opposition,  and 
the  earth  between  them. 

873.  SOLAR  ECLIPSES. — When  the  moon  passes  between 
the  earth  and  sun,  there  happens  an  eclipse  of  the  sun,  be- 
cause then  the  moon's  shadow  falls  upon  the  earth.  A  total 
eclipse  of  the  sun  happens  often,  but  when  it  occurs,  the  to- 
tal obscurity  is  confined  to  a  small  part  of  the  earth ;  since 
the  dark  portion  of  the  moon's  shadow  never  exceeds  200 
miles  in  diameter  on  the  earth.  But  the  moon's  partial 
shadow,  or  penumbra,  may  cover  a  space  on  the  earth  of 
more  than  4000  miles  in  diameter,  within  all  which  space 
the  sun  will  be  more  or  less  eclipsed.  When  the  penumbra 
first  touches  the  earth,  the  eclipse  begins  at  that  place,  and 
ends  when  the  penumbra  leaves  it.  But  the  eclipse  will  be 
total  only  where  the  dark  shadow  of  the  moon  touches  the 
earth. 

Fig.  218. 


Fig.  218  represents  an  eclipse  of  the  sun,  without  regard 
to  the  penumbra,  that  it  may  be  observed  how  small  a  part  of 
the  earth  the  dark  shadow  of  the  moon  covers.  To  those 

Why  is  the  same  eclipse  total  at  one  place,  and  only  partial  at 
another  1  Why  is  a  total  eclipse  of  the  sun  confined  to  so  small  a  part  of 
the  earth  1  What  is  meant  by  penumbra?  What  will  be  the  difference 
in  the  aspect  of  the  eclipse,  whether  the  observer  stands  within  the  dark 
shadow,  or  only  within  the  penumbra  1 


ECLIPSES.  291 

who  live  within  the  limits  of  this  shadow,  the  eclipse  will  be 
total,  while  to  those  who  live  in  any  direction  around  it,  and 
within  reach  of  the  penumbra,  it  will  be  only  partial. 

874.  Solar  eclipses  are  called  annular,  from  annulus,  a 
ring,  when  the  moon  passes  across  the  centre  of  the  sun, 
hiding  all  his  light,  with  the  exception  of  a  ring  on  his  outer 
edge,  which  the  moon  is  too  small  to  cover  from  the  position 
in  which  it  is  seen. 

Fig.  219. 


Fig.  219  represents  a  solar  eclipse,  with  the  penumbra  D, 
C,  and  the  umbra,  or  dark  shadow,  as  seen  in  the  above  figure. 

When  the  moon  is  at  its  greatest  distance  from  the  earth, 
its  shadow  m  o,  sometimes  terminates,  before  it  reaches  the 
earth,  and  then  an  observer  standing  directly  under  the  point 
o,  will  see  the  outer  edge  of  the  sun,  forming  a  bright  ring 
around  the  circumference  of  the  moon,  thus  forming  an  an- 
nular eclipse. 

The  penumbra  D  C,  is  only  a  partial  interception  of  the 
sun's  rays,  and  in  annular  eclipses  it  is  this  partial  shadow 
only  which  reaches  the  earth,  while  the  umbra,  or  dark 
shadow,  terminates  in  the  air.  Hence  annular  eclipses  are 
never  total  in  any  part  of  the  earth.  The  penumbra,  as  al- 
ready stated,  may  cover  more  than  4000  miles  of  space, 
while  the  umbra  never  covers  more  than  200  miles  in  di- 
ameter ;  hence  partial  eclipses  of  the  sun  may  be  seen  by  a 
vast  number  of  inhabitants,  while  comparatively  few  will 
witness  the  total  eclipse. 

875.  When  there  happens  a  total  solar  eclipse  to  us,  we 
are  eclipsed  to  the  moon,  and  when  the  moon  is  eclipsed  to 
us,  an  eclipse  of  the  sun  happens  to  the  rnoon.  To  the  moon, 
an  eclipse  of  the  earth  can  never  be  total,  since  her  shadow 
covers  only  a  small  portion  of  the  earth's  surface.  Such  an 
eclipse,  therefore,  at  the  moon,  appears  only  as  a  dark  spot 
on  the  face  of  the  earth;  but  when  the  moon  is  eclipsed  to 

What  is  meant  by  annular  eclipses  1  Are  annular  eclipses  ever  total 
in  any  part  of  the  earth  1  In  annular  eclipses,  what  part  of  the  moon's 
shadow  reaches  the  earth!  What  is  said  concerning  eclipses  of  the 
earth,  as  seen  from  the  moon  1 


.• 

292  TIDES. 

us,  the  sun  is  partially  eclipsed  to  the  moon  for  several  hours 
longer  than  the  moon  is  eclipsed  to  us. 
THE  TIDES. 

876.  The  ebbing  and  flowing  of  the  sea,  which  regularly 
takes  place  twice  in  24  hours,  are  called  the  tides.  The 
cause  of  the  tides,  is  the  attraction  of  the  sun  and  moon,  but 
chiefly  of  the  moon,  on  the  waters  of  the  ocean.  In  virtue 
of  the  universal  principle  of  gravitation,  heretofore  explained, 
the  moon,  by  her  attraction,  draws,  or  raises  the  water  to- 
wards her,  but  because  the  power  of  attraction  diminishes 
as  the  squares  of  the  distances  increase,  the  waters,  on  the 
opposite  side  of  the  earth,  are  not  so  much  attracted  as  they 
are  on  the  side  nearest  the  moon.  This  want  of  attraction, 
together  with  the  greater  centrifugal  force  of  the  earth  on  its 
opposite  side,  produced  in  consequence  of  its  greater  distance 
from  the  common  centre  of  gravity,  between  the  earth  and 
moon,  causes  the  waters  to  rise  on  the  opposite  side,  at  the 
same  time  that  they  are  raised  by  direct  attraction  on  the 
side  nearest  the  moon. 

Thus  the  waters  are  constantly  elevated  on  the  sides  of  the 
earth  opposite  to  each  other  above  their  common  level,  and 
consequently  depressed  at  opposite  points  equally  distant  from 
these  elevations. 

Let  m,  fig.  220,  be  the  moon,  and  E  the  earth  covered  with 
Fig.  220. 


water.  As  the  moon  passes  round  the  earth,  its  solid  and 
fluid  parts  are  equally  attracted  by  her  influence  according 
to  their  densities  ;  but  while  the  solid  parts  are  at  liberty  to 
move  only  as  a  whole,  the  water  obeys  the  slightest  impulse, 
and  thus  tends  towards  the  moon  where  her  attraction  is  the 
strongest.  Consequently,  the  waters  are  perpetually  ele- 
vated immediately  under  the  moon.  If,  therefore,  the  earth 
stood  still,  the  influence  of  the  moon's  attraction  would  raise 
the  tides  only  as  she  passed  round  the  earth.  But  as  the 

What  are  the  tides  ?  What  is  the  cause  of  the  tides  1   What  causes 
the  tide  to  rise  on  the  side  of  the  earth  opposite  to  the  moon  1 


TIDES.  293 

earth  turns  on  her  axis  every  24  hours,  and  as  the  waters 
nearest  the  moon,  as  at  a,  are  constantly  elevated,  they  will, 
in  the  course  of  24  hours,  move  round  the  whole  earth,  and 
consequently  from  this  cause  there  will  be  high  water  at 
every  place  once  in  24  hours.  As  the  elevation  of  the  wa- 
ters under  the  moon  causes  their  depression  at  90  degrees 
distance  on  the  opposite  sides  of  the  earth,  d  and  ct  the  point 
c  will  come  to  the  same  place,  by  the  earth's  diurnal  revolu- 
tion, six  hours  after  the  point  a,  because  c  is  one  quarter  of 
the  circumference  of  the  earth  from  the  point  a,  and  there- 
fore there  will  be  low  water  at  any  given  place  six  hours 
after  it  was  high  water  at  that  place.  But  while  it  is  high 
water  under  the  moon,  in  consequence  of  her  direct  attrac- 
tion, it  is  also  high  water  on  the  opposite  side  of  the  earth 
in  ftonsequence  of  her  diminished  attraction,  and  the  earth's 
centrifugal  motion,  and  therefore  it  will  be  high  water  from 
this  cause  twelve  hours  after  it  was  high  water  from  the 
former  cause,  and  six  hours  after  it  was  low  water  from  both 
causes. 

Thus,  when  it  is  high  water  at  a  and  b,  it  is  low  water  at 
c  and  d,  and  as  the  earth  revolves  once  in  24  hours,  there 
will  be  an  alternate  ebbing  and  flowing  of  the  tide,  at  every 
place,  once  in  six  hours. 

But  while  the  earth  turns  on  her  axis,  the  moon  advances 
in  her  orbit,  and  consequently  any  given  point  on  the  earth 
will  not  come  under  the  moon  on  one  day  so  soon  as  it  did 
on  the  day  before.  For  this  reason,  high  or  low  water  at 
any  place  comes  about  fifty  minutes  later  on  one  day  than  it 
did  the  day  before. 

Thus  far  we  have  considered  no  other  attractive  influence 
sxcept  that  of  the  moon,  as  affecting  the  waters  of  the  ocean. 
But  the  sun,  as  already  observed,  has  an  effect  upon  the 
tides,  though  on  account  of  his  great  distance,  his  influence  is 
small  when  compared  with  that  of  the  moon. 

877.  When  the  sun  and  moon  are  in  conjunction,  as  repre- 
sented in  fig.  220,  which  takes  place  at  her  change,  or  when 
Jhey  are  in  opposition,  which  takes  place  at  full  moon,  then 
their  forces  are  united,  or  act  on  the  waters  in  the  same  di- 

If  the  earth  stood  still,  the  tides  would  rise  only  as  the  moon  passes 
round  the  earth  ;  what  then  causes  the  tides  to  rise  twice  in  24  hours  1 
When  it  is  high  water  under  the  moon  by  her  attraction,  what  is  the 
cause  of  high  water  on  the  opposite  side  of  the  earth,  at  the  same  time  ? 
Why  are  the  tides  about  fifty  minutes  later  every  day1?  What  pro- 
duces spring  tides  1  Where  must  the  moon  be  in  respect  to  the  sun,  to 
produce  spring  tides'? 

35* 


294  LATITUDE  AND  LONGITUDE. 

rection,  and  consequently  the  tides  are  elevated  higher  than 
usual,  and  on  this  account  are  called  spring  tides. 

878.  But  when  the  moon  is  in  her  quadratures,  or  quar- 
ters, the  attraction  of  the  sun  tends  to  counteract  that  of  the 
moon,  and  although  his  attraction  does  not  elevate  the  waters 
and  produce  tides,  his  influence  diminishes  that  of  the  moon, 
and  consequently  the  elevation  of  the  waters  are  less  when 
the  sun  and  moon  are  so  situated  in  respect  to  each  other, 
than  when  they  are  in  conjunction,  or  opposition. 
Fig.  221. 


This  effect  is  represented  by  fig.  221,  where  the  elevation 
of  the  tides  at  c  and  d  is  produced  by  the  causes  already  ex- 
plained; but  their  elevation  is  not  so  great  as  in  fig.  220, 
since  the  influence  of  the  sun  acting  in  the  direction  a  bt 
tends  to  counteract  the  moon's  attractive  influence.  These 
small  tides  are  called  neap  tides,  and  happen  only  when  the 
moon  is  in  her  quadratures. 

The  tides  are  not  at  their  greatest  heights  at  the  time 
when  the  moon  is  at  its  meridian,  but  some  time  afterwards, 
because  the  water,  having  a  motion  forward,  continues  to 
advance  by  its  own  inertia,  some  time  after  the  direct  influ- 
ence of  the  moon  has  ceased  to  affect  it. 

LATITUDE  AND  LONGITUDE. 

879.  Latitude  is  the  distance  from  the  equator  in  a  direct 
line,  north  or  south,  measured  in  degrees  and  minutes.  The 
number  of  degrees  is  90  north,  and  as  many  south,  each  line 
on  which  these  degrees  are  reckoned  running  from  the  equa- 
tor to  the  poles.  Places  at  the  north  of  the  equator  are  in 
north  latitude,  and  thdse  south  of  the  equator  are  in  south  lati- 
tude. The  parallels  of  latitude  are  imaginary  lines  drawn 
parallel  to  the  equator,  either  north  or  south,  and  hence 
every  place  situated  on  the  same  parallel,  is  in  the  same 
latitude,  because  every  such  place  must  be  at  the  same  dis- 

What  is  the  occasion  of  neap  tides'?  What  is  latitude?  How  many 
degrees  of  latitude  are  there  1  How  far  do  the  lines  of  latitude  extend  ? 
What  is  meant  by  north  and  south  latitude?  What  are  the  parallels  of 
latitude  1 


LATITUDE  AND  LONGITUDE. 


295 


tance  from  the  equator.     The  length  of  a  degree  of  latitude 
is  60  geographical  miles. 

880.  Longitude  is  the  distance  measured  in  degrees  and 
minutes,  either  east  or  west,  from  any  given  point  on  the 
equator,  or  on  any  parallel  of  latitude.  Hence  the  lines,  or 
meridians  of  longitude,  cross  those  of  latitude  at  right  an* 
gles.  The  degrees  of  longitude  are  180  in  number,  its  lines 
extending  half  a  circle  to  the  east,  and  half  a  circle  to  the 
west,  from  any  given  meridian,  so  as  to  include  the  whole 
circumference  of  the  earth.  A  degree  of  longitude,  at  the 
equator,  is  of  the  same  length  as  a  degree  of  latitude,  but  as 
the  poles  are  approached,  the  degrees  of  longitude  diminish 
in  length,  because  the  earth  grows  smaller  in  circumference 
from  the  equator  towards  the  poles ;  hence  the  lines  sur- 
rounding it  become  less  and  less.  This  will  be  made  obvi- 
ous by  fig.  222. 

Let  this  figure  represent  the 
earth,  N  being  the  north  pole, 
S  the  south  pole,  and  E  W  the 
equator.  The  lines  10,  20,  30, 
and  so  on,  are  the  parallels  of 
latitude,  and  the  lines  N  a  S, 
N  b  S,  fyc.,  are  meridian  lines, 
or  those  of  longitude. 

The  latitude  of  any  place  on 
the  globe,  is  the  number  of  de- 
grees between  that  place  and 
the  equator,  measured  on  a 
meridian  line ;  thus,  x  is  in  lat. 
40  degrees,  because  the  x  g 
part  of  the  meridian  contains  40  degrees. 

The  longitude  of  a  place  is  the  number  of  degrees  it  is 
situated  east  or  west  from  any  meridian  line ;  thus,  v  is  20 
degrees  west  longitude  from  z,  and  x  is  20  degrees  east  Ion* 
gitude  from  v. 

881.  As  the  equator  divides  the  earth  into  two  equal  parts, 
or  hemispheres,  there  seems  to  be  a  natural  reason  why  the 
degrees  of  latitude  should  be  reckoned  from  this  great  circle. 
But  from  east  to  west  there  is  no  natural  division  of  the 
earth,  each  meridian  line  being  a  great  circle,  dividing  the 
earth  into  two  hemispheres,  and  hence  there  is  no  natural 


is  longitude'?    How  many  degrees  of  longitude  are  there,  east 
I  What  is  the  latitude  of  any  pU      "  — 


What 

*r  west  1  What  is  the  latitude  of  any  place  1  What  is  the  longitude  of 
a  place  1  Why  are  the  degrees  of  latitude  reckoned  from  the  equator  1 


296          LATITUDE  AND  LONGITUDE. 

reason  why  longitude  should  be  reckoned  from  one  meridian 
any  more  than  another.  It  has,  therefore,  been  customary  for 
writers  and  mariners  to  reckon  longitude  from  the  capital  of 
their  own  country,  as  the  English  from  London,  the  French 
from  Paris,  and  the  Americans  from  Washington.  But  this 
mode,  it  is  apparent,  must  occasion  much  confusion,  since 
each  writer  of  a  different  nation  would  be  obliged  to  correct 
die  longitude  of  all  other  countries,  to  make  it  agree  with  his 
own.  More  recently,  therefore,  the  writers  of  Europe  and 
America  have  selected  the  royal  observatory,  at  Greenwich, 
near  London,  as  the  first  meridian,  and  on  most  maps  and 
charts  lately  published,  longitude  is  reckoned  from  that  place 

882.  How  Latitude  is  found. — The  latitude  of  any  place 
is  determined  by  taking  the  altitude  of  the  sun  at  mid-day, 
and  then  subtracting  this  from  90  degrees,  making  proper 
allowances  for  the  sun's  place  in  the  heavens.     The  reason 
of  this  will  be  understood,  when  it 'is  considered  that  the 
whole  number  of  degrees  from  the  zenith  to  the  horizon  is 
90,  and  therefore  if  we  ascertain  the  sun's  distance  from  the 
horizon,  that  is,  his  altitude,  by  allowing  for  the  sun's  de- 
clination north  or  south  of  the  equator,  and  substracting  this 
from  the  whole  number,  the  latitude  of  the  place  will  be 
found.     Thus,  suppose  that  on  the  20th  of  March,  when  the 
sun  is  at  the  equator,  his  altitude  from  any  place  north  of  the 
equator  should  be  found  to  be  48  degrees  above  the  horizon  ] 
this,  substracted  from  90,  the  whole  number  of  the  degrees  of 
latitude,  leaves  42,  which  will  be  the  latitude  of  the  place 
where  the  observation  was  made. 

883.  If  the  sun,  at  the  time  of  observation,  has  a  declina- 
tion north  or  south  of  the  equator,  this  declination  must  be 
added  to,  or  substracted  from,  the  meridian  altitude,  as  the  case 
may  be.      For  instance,  another  observation  being  taken  at 
the  place  where  the  latitude  was  found  to  be  42,  when  the 
sun  had  a  declination  of  8  degrees  north,  then  his  altitude 
would  be  8  degrees  greater  than  before,  and  therefore  56, 
instead  of  48.     Now,  substracting  this  8,  the  sun's  declina- 
tion, from  56,  and  the  remainder  from  90,  and  the  latitude  of 

What  is  said  concerning  the  places  from  which  the  degrees  of  longi- 
tude have  been  reckoned  1  What  is  the  inconvenience  of  estimating 
longitude  from  a  place  in  each  country  ?  From  what  place  is  longitude 
reckoned  in  Europe  and  America  1  How  is  the  latitude  of  a  place  de- 
termined'? Give  an  example  of  the  method  of  finding  the  latitude  of  the 
same  place  at  different  seasons  of  the  year.  When  must  the  sun's  de- 
clination from  the  equator  be  added  to,  and  when  substracted  from,  his 
meridian  altitude? 


LATITUDE  AND  LONGITUDE.  297 

the  place  will  be  found  42,  as  before.  If  the  sun's  declina- 
tion be  south  of  the  equator,  and  the  latitude  of  the  place 
north,  his  declination  must  be  added  to  the  meridian  altitude 
instead  of  being  substracted  from  it.  The  same  result  may 
be  obtained  by  taking  the  meridian  altitude  of  any  of  the  fixed 
=?tars,  whose  declinations  are  known,  instead  of  the  sun's,  and 
proceeding  as  above  directed. 

884.  How  Longitude  is  found. — There  is  more  difficulty 
in  ascertaining  the  degrees  of  longitude,  than  those  of  latitude, 
because,  as  above  stated,  there  is  no  fixed  point,  like  that  of 
the  equator,  from  which  its  degrees  are  reckoned.     The  de- 
grees of  longitude  are  therefore  estimated  from  Greenwich, 
and  are  ascertained  by  the  following  methods  : — 

885.  When  the  sun  comes  to  the  meridian  of  any  place,  it 
is  noon,  or  12  o'clock,  at  that  place,  and  therefore,  since  the 
equator  is  divided  into  360  equal  parts,  or  degrees,  and  since 
the  earth  turns  on  its  axis  once  in  24  hours,  15  degrees  of 
the  equator  will  correspond  with  one  hour  of  time,  for  360 
degrees   being  divided   by  24  hours,  will   give  15.       The 
earth,  therefore,  moves  in  her  daily  revolution,  at  the  rate 
of  15  degrees  for  every  hour  of  time.     Now,  as  the  appa- 
rent course  of  the  sun  is  from  east  to  west,  it  is  obvious  that 
he  will  come  to  any  meridian  lying  east  of  a  given  place, 
sooner  than  to  one  lying  west  of  that  place,  and  therefore  it 
will  be  12  o'clock  to  the  east  of  anyplace,  sooner  than  at 
that  place,  or  to  the  west  of  it.     When,  therefore,  it  is  noon 
at  any  one  place,  it  will  be  1  o'clock  at  all  places  15  degrees 
to  the  east  of  it,  because  the  sun  was  at  the  meridian  of  such 
places  an  hour  before ;  and  so,  on  the  contrary,  it  will  be 
eleven  o'clock,  fifteen  degrees  west  of  the  same  place,  be- 
cause the  sun  has  still  an  hour  to  travel  before  he  reaches  the 
meridian  of  that  place.     It  makes  no  difference,  then,  where 
the  observer  is  placed,  since,  if  it  is  12  o'clock  where  he  is,  it 
will  be  1    o'clock  15  degrees  to  the  east  of  him,  and  11 
o'clock  15  degrees  to  the  west  of  him,  and  so  in  this  propor- 
tion, let  the  time  be  more  or  less.     Now,  if  any  celestial  phe- 
nomenon should  happen,  such  as  an  eclipse  of  the  moon,  or 
of  Jupiter's  satellites,  the  difference  of  longitude  between 
two  places  where  it  is  observed,  may  be  determined  by  the 

Why  is  there  more  difficulty  in  ascertaining  the  degrees  of  longitude 
than  of  latitude  "?  How  many  degrees  of  longitude  does  the  surface  of 
the  earth -pass  through  in  an  hour?  Suppose  it  is  noon  at  any  given 
place,  what  o'clock  will  it  be  15  degrees  to  the  east  of  that  placed  Ex- 
pluin  the  reason.  How  may  longitude  be  determined  by  an  eclipse  7 


298  LATITUDE  AND  LONGITUDE, 

difference  of  ihe  times  at  which  it  appeared  to  take  place. 
Thus,  if  the  moon  enters  the  earth's  shadow  at  6  o'clock  in 
the  evening-,  as  seen  at  Philadelphia,  and  at  half  past  6 
o'clock  at  another  place,  then  this  place  is  half  an  hour,  01 
7£  degrees,  to  the  east  of  Philadelphia,  because  1\  degrees 
of  longitude  are  equal  to  half  an  hour  of  time.  To  apply 
these  observations  practically,  it  is  only  necessary  that  it 
should  be  known  exactly  at  what  time  the  eclipse  takes  place 
at  a  given  point  on  the  earth. 

886.  Longitude  is  also  ascertained  by  means  of  a  chro- 
nometer, or  true  time  piece,  adjusted  to  any  given  meridian; 
for  if  the  difference  between  two  clocks,  situated  east  and 
west  of  each  other,  and  going  exactly  at  the  same  rate,  can 
be  known  at  the  same  time,  then  the  distance  between  the 
two  meridians,  where  the  clocks  are  placed  will  be  known, 
and  the  difference  of  longitude  may  be  found. 

Suppose  two  chronometers,  which  are  known  to  go  at  ex- 
actly the  same  rate,  are  made  to  indicate  12  o'clock  by  the 
meridian  line  of  Greenwich,  and  the  one  be  taken  to  sea, 
while  the  other  remains  at  Greenwich.  Then  suppose  the 
captain,  who  takes  his  chronometer  to  sea,  has  occasion  to 
know  his  longitude.  In  the  first  place,  he  ascertains,  by  an 
observation  of  the  sun,  when  it  is  12  o'clock  at  the  place 
where  he  is,  and  then  by  his  time  piece,  when  it  is  12  o'clock 
at  Greenwich,  and  by  allowing  15  degrees  for  every  hour 
of  the  difference  in  time,  he  will  know  his  precise  longitude 
in  any  part  of  the  world.  For  example,  suppose  the  cap- 
tain sails  with  his  chronometer  for  America,  and  after  being 
several  weeks  at  sea,  finds  by  observation  that  it  is  12  o'clock 
by  the  sun,  and  at  the  same  time  finds  by  his  chronometer, 
that  it  is  4  o'clock  at  Greenwich.  Then  because  it  is  noon 
at  his  place  of  observation  after  it  is  noon  at  Greenwich,  he 
knows  that  his  longitude  is  west  from  Greenwich,  and  by  al- 
lowing 15  degrees  for  every  hour  of  the  difference,  his  lon- 
gitude is  ascertained.  Thus,  15  degrees,  multiplied  by  4 
hours,  give  60  degrees  of  west  longitude  from  Greenwich. 
If  it  is  noon  at  the  place  of  observation,  before  it  is  noon  at 
Greenwich,  then  the  captain  knows  that  his  longitude  is  east, 
and  his  true  place  is  found  in  the  same  manner. 

Explain  the  principles  on  which  longitude  is  determined  by  the  chro- 
nometer. Suppose  the  captain  finds  "by  his  chronometer  that  it  is  12 
o'clock,  where  he  is,  six  hours  later  than  at  Greenwich,  what  then 
would  be  his  longitude  1  Suppose  he  finds  it  to  be  12  o'clock  4  hours 
earlier,  where  he  is,  than  at  Greenwich,  what  then  would  be  his  lon- 
gitude ? 


FIXED  STARS.  299 

FIXED  STARS. 

887.  The  stars  are  called  fixed,  because  they  have  been 
observed  not  to  change  their  places  with  respect  to  each 
other.     They  may  be  distinguished  by  the  naked  eye  from 
the  planets  of  our  system  by  their  scintillations,  or  twinkling. 
The  stars  are  divided  into  classes,  according  to  their  magni- 
tudes, and  are  called  stars  of  the  first,  second,  and  so  on  to 
the  sixth  magnitude.     About  2000  stars  may  be  seen  with 
the  naked  eye  in  the  whole  vault  of  the  heavens,  though 
only  about  1000  are  above  the  horizon  at  the  same  time.    Of 
these,  about  17  are  of  the  first  magnitude,  50  of  the  2d  mag- 
nitude, and  150  of  the  3d  magnitude.     The  others  are  of  the 
4th,  5th,  and  6th  magnitudes,  the  last  of  which  are  the 
smallest  that  can  be  distinguished  with  the  naked  eye. 

888.  It  might  seem  incredible,  that  on  a  clear  night  only 
about  1000  stars  are  visible,  when  on  a  single  glance  at  the 
different  parts  of  the  firmament,  their  numbers  appear  innu- 
merable.    But  this  deception  arises  from  the  confused  and 
hasty  manner  in  which  they  are  viewed,  for  if  we  look  stea- 
dily on  a  particular  portion  of  sky,  and  count  the  stars  con- 
tained within  certain  limits,  we  shall  be  surprised  to  find 
their  number  so  few. 

889.  As  we  have  incomparably  more  light  from  the  moon 
than  from  all  the  stars  together,  it  is  absurd  to  suppose  that 
they  were  made  for  no  other  purpose  than  to  cast  so  faint  a 
glimmering  on  our  earth,  and  especially  as  a  great  propor- 
tion of  them  are  invisible  to  our  naked  eyes.      The  nearest 
fixed  stars  to  our  system,  from  the  most  accurate  astronomi- 
cal calculations,  cannot  be  nearer  than  20,000,000,000,000, 
or  20  trillions  of  miles  from  the  earth,  a  distance  so  immense, 
that  light  cannot  pass  through  it  in  less  than  three  years. 
Hence,  were  these  stars  annihilated  at  the  present  time,  their 
light  would  continue  to  flow  towards  us,  and  they  would  ap- 
pear to  be  in  the  same  situation  to  us,  three  years  hence,  that 
they  do  now. 

890.  Our  sun,  seen  from  the  distance  of  the  nearest  fixed 
stars,  would  appear  no  larger  than  a  star  of  the  first  magni- 

Why  are  the  stars  called  fixed  1  How  may  the  stars  be  distinguished 
from  the  planets  1  The  stars  are  divided  into  classes,  according  to  their 
magnitudes;  how  many  classes  are  there  1  How  many  stars  may  be 
seen  with  the  naked  eye,  in  the  whole  firmament  1  Why  does  there  ap- 
pear to  be  more  stars  than  there  really  are?  What  is  the  computed  dis- 
tance of  the  nearest  fixed  stars  from  the  earth1?  How  long  would  it 
take  light  to  reach  us  from  the  fixed  stars  1  How  large  would  our  sun 
appear  at  the  distance  of  the  fixed  stars  1 


300  COMETS. 

tude  does  to  us.  These  stars  appear  no  larger  to  us,  when 
the  earth  is  in  that  part  of  her  orbit  nearest  to  them,  than 
they  do,  when  she  is  in  the  opposite  part  of  her  orbit ;  and  as 
our  distance  from  the  sun  is  95,000,000  of  miles,  we  must 
be  twice  this  distance,  or  the  whole  diameter  of  the  earth's 
orbit,  nearer  a  given  fixed  star  at  one  period  of  the  year 
than  at  another.  The  difference,  therefore,  of  190,000,000 
of  miles,  bears  so  small  a  proportion  to  the  whole  distance  be- 
tween us  and  the  fixed  stars,  as  to  make  no  appreciable  dif- 
ference in  their  sizes,  even  when  assisted  by  the  most  power- 
ful telescopes. 

89 1.  The  amazing  distances  of  the  fixed  stars  may  also  be 
inferred  from  the  return  of  comets  to  our  system,  after  an  ab- 
sence of  several  hundred  years. 

The  velocity  with  which  some  of  these  bodies  move,  when 
nearest  the  sun,  has  been  computed  at  nearly  a  million  of 
miles  in  an  hour,  and  although  their  velocities  must  be  per- 
petually retarded,  as  they  recede  from  the  sun,  still,  in  250 
years  of  time,  they  must  move  through  a  space  which  to  us 
would  be  infinite.  The  periodical  return  of  one  comet  is 
known  to  be  upwards  of  500  years,  making  more  than  250 
years  in  performing  its  journey  to  the  most  remote  part  of 
its  orbit,  and  as  many  in  returning  back  to  our  system ;  and 
that  it  must  still  always  be  nearer  our  system  than  the  fixed 
stars,  is  proved  by  its  return;  for  by  the  laws  of  gravitation, 
did  it  approach  nearer  another  system  it  would  never  again 
return  to  ours. 

From  such  proofs  of  the  vast  distances  of  the  fixed  stars, 
there  can  be  no  doubt  that  they  shine  with  their  own  lighf, 
like  our  sun,  and  hence  the  conclusion  that  they  are  suns  t j 
other  worlds,  which  move  around  them,  as  the  planets  do 
around  our  sun.  Their  distances  will,  however,  prevent  our 
ever  knowing,  except  by  conjecture,  whether  this  is  the  case 
or  not,  since,  were  they  millions  of  times  nearer  us  than  they 
are,  we  should  not  be  able  to  discover  the  reflected  light  of 
their  planets. 

COMETS. 

892.  Besides  the  planets,  which  move  round  the  sun  in 
regular  order  and  in  nearly  circular  orbits,  there  belongs  to 

What  is  said  concerning  the  difference  of  the  distance  between  the 
earth  and  the  fixed  stars  at  different  seasons  of  the  year,  and  of  their 
different  appearance  in  consequence'?  How  may  the  distances  of  the 
fixed  stars  be  inferred,  by  the  long  absence  and  return  of  comets  1  On 
what  grounds  is  it  supposed  that  the  fixed  stars  are  suns  to  other  worlds'? 


COMETS.  301 

the  solar  system  an  unknown  number  of  bodies  called 
Comets,  which  move  round  the  sun  in  orbits  exceedingly  ec- 
centric, or  elliptical,  and  whose  appearance  among  our 
heavenly  bodies  is  only  occasional.  Comets,  to  the  naked 
eye,  have  no  visible  disc,  but  shine  with  a  faint,  glimmering 
light,  and  are  accompanied  by  a  train  or  tail,  turned  from 
the  sun,  and  which  is  sometimes  of  immense  length.  They 
appear  in  every  region  of  the  heavens,  and  move  in  every 
possible  direction. 

In  the  days  of  ignorance  and  superstition,  comets  were 
considered  the  harbingers  of  war,  pestilence,  or  some  other 
great  or  general  evil ;  and  it  was  not  until  astronomy  had 
made  considerable  progress  as  a  science,  that  these  stran- 
gers could  be  seen  among  our  planets  without  the  expecta- 
tion of  some  direful  event. 

893.  It  had  been  supposed  that  comets  moved  in  straight 
lines,  coming  from,  the  regions  of  infinite,  or  unknown  space, 
and  merely  passing  by  our  system,  on  their  way  to  regions 
equally  unknown  and  infinite,  and  from  which  they  never 
returned.      Sir  Isaac   Newton  was  the  first  to  demonstrate 
that  the  comets  pass  round  the  sun,  like  the  planets,  but  that 
their  orbits  are  exceedingly  elliptical,  and  extend  out  to  a 
vast  distance  beyond  the  solar  system. 

894.  The  number  of  comets  is  unknown,  though  some  as- 
tronomers suppose  that  there  are  nearly  500  belonging  to 
our   system.      Ferguson,  who   wrote  in  about   1760,  sup- 
posed that  there  were  less  than  30  comets  which  made  us 
occasional  visits ;  but  since  that  period  the  elements  of  the 
orbits  of  nearly  100  of  these  bodies  have  been  computed. 

Of  these,  however,  there  are  only  three  whose  periods  of 
return  among  us  are  known  with  any  degree  of  certainty. 
The  first  of  these  has  a  peri- 
od  of  75  years ;  the  second  a| 
period  of  129  years;  and  the 
third  a  period  of  575  years,  j 
The  third  appeared  in"l  680, 1 
and  therefore  cannot  be  ex- 
pected again  until  the  year] 
2225.  This  comet,  fig. 
223,  in  1680,  excited  the' 

What  number  of  comets  are  supposed  to  belong  to  our  system  1  How 
many  have  had  the  elements  of  their  orbits  estimated  by  astronomers! 
How  many  are  there  whose  periods  of  return  are  known?  What  is 
said  of  the  com -t  of  10801 

96 


302  ELECTRICITY. 

most  intense  interest  among  the  astronomers  of  Europe,  on 
account  of  its  great  apparent  size  and  near  approach  to  onr 
system.  In  the  most  remote  part  of  its  orbit,  its  dis- 
tance from  the  sun  was  estimated  at  about  eleven  thou- 
sand two  hundred  millions  of  miles.  At  its  nearest  ap- 
proach to  the  sun,  which  was  only  about  50,000  miles,  its 
velocity,  according  to  Sir  Isaac  Newton,  was  880,000  miles 
in  an  hour  ;  and  supposing  it  to  have  retained  the  sun's  neat, 
like  other  solid  bodies,  its  temperature  must  have  been  about 
2000  times  that  of  red  hot  iron.  The  tail  of  this  comet  was 
at  least  100  millions  of  miles  long. 

895.  In  the  Edinburgh  Encyclopedia,  article  Astronomy, 
there  is  the  most  complete  table  of  comets  yet  published. 
This  table  contains  the  elements  of  97  comets,  calculated  by 
different  astronomers,  down  to  the  year  1808. 

From  this  table  it  appears  that  24  comets  have  passed  be- 
tween the  sun  and  the  orbit  of  Mercury ;  33  between  the 
orbits  of  Venus  and  the  Earth ;  15  between  the  orbits  of  the 
Earth  and  Mars  ;  3  between  the  orbits  of  Mars  and  Ceres ; 
and  1  between  the  orbits  of  Ceres  and  Jupiter.  It  also  ap- 
pears by  this  table  that  49  comets  have  moved  round  the 
sun  from  west  to  east,  and  48  from  east  to  west. 

896.  Of  the  nature  of  these  wandering  planets  very  little  is 
known.     When  examined  by  a  telescope,  they  appear  like  a 
mass  of  vapours  surrounding  a  dark  nucleus.     When  the 
comet  is  at  its  perihelion,  or  nearest  the  sun,  its  colour  seems 
to  be  heightened  by  the  intense  light  or  heat  of  that  luminary, 
and  it  then  often  shines  with  more  brilliancy  than  the  planets. 
At  this  time  the  tail  or  train,  which  is  always  directly  oppo- 
site to  the  sun,  appears  at  its  greatest  length,  but  is  com- 
monly so  transparent  as  to  permit  the  fixed  stars  to  be  seen 
through  it.     A  variety  of  opinions  have  been  advanced  by 
astronomers  concerning   the   nature   and   causes   of  these 
trains.     Newton  supposed  that  they  were  thin  vapour,  made 
to  ascend  by  the  sun's  heat,  as  the  smoke  of  a  fire  ascends 
from  the  earth  ;  while  Kepler  maintained  that  it  was  the 
atmosphere  of  the  comet  driven  behind  it  by  the  impulse  of 
the  sun's  rays.     Others  suppose  that  this  appearance  arises 
from   streams  of  electric   matter   passing  away   from   the 
comet,  &c. 

ELECTRICITY. 

897.  The  science  of  Electricity,  which  now  ranks  as  an 
important  branch  of  Natural  Philosophy,  is  wholly  of  mo- 


ELECTRICITY.  30d 

dern  date.  The  ancients  were  acquainted  with  a  few  de- 
lached  facts  dependent  on  the  agency  of  electrical  influence, 
but  they  never  imagined  that  it  was  extensively  concerned 
in  the  operations  of  nature,  or  that  it  pervaded  material  sub- 
stances generally.  The  term  electricity  is  derived  from  elec- 
tron, the  Greek  name  of  amber,  because  it  was  known  to  the 
ancients,  that  when  that  substance  was  rubbed  or  excited,  it 
attracted  or  repelled  small  light  bodies,  and  it  was  then  un- 
known that  other  substances  when  excited  would  do  the  same. 

898.  When  a  piece  of  glass,  sealing  wax,  or  amber,  is 
rubbed  with  a  dry  hand,  and  held  towards  small  and  light 
bodies,  such  as  threads,  hairs,  feathers,  or  straws,  these  bo- 
dies will  fly  towards  the  surface  thus  rubbed,  and  adhere  to 
it  for  a  short  time.     The  influence  by  which  these  small  sub- 
stances are  drawn,  is  called  electrical  attraction  ;  the  sur- 
face having  this  attractive  power  is  said  to  be  excited ;  and 
the  substances  susceptible  of  this  excitation,  are  called  elec- 
trics.     Substances  not  having  this  attractive  power  when 
rubbed,  are  called  non-electrics. 

899.  The  principal  electrics  are  amber,  rosin,  sulphur, 
glass,  the  precious  stones,  sealing  wax,  and  the  fur  of  quad- 
rupeds.    But  the  metals,  and  many  other  bodies,  may  be  ex- 
cited when  insulated  and  treated  in  a  certain  manner. 

After  the  light  substances  which  had  been  attracted  by  the 
excited  surface,  have  remained  in  contact  with  it  a  short 
time,  the  force  which  brought  them  together  ceases  to  act,  or 
acts  in  a  contrary  direction,  and  the  light  bodies  are  repelled, 
or  thrown  away  from  the  excited  surface.  Two  bodies,  also, 
which  have  been  in  contact  with  the  excited  surface,  mutually 
repel  each  other. 

900.  Various  modes  have  been  devised  for  exhibiting  dis 
tinctly  the  attractive  and  repulsive  agencies  of  electricity,  and 
for  obtaining  indications  of  its  presence,  when  it  exists  only 
in  a  feeble  degree.     Instruments  for  this  purpose  are  termed 
Electroscopes. 

901.  One  of  the  simplest  instruments  of  this  kind  consists 
of  a  metallic  needle,  terminated  at  each  end  by  a  light  pith 
ball,  which  is  covered   with  gold  leaf,  and  supported  hori- 
zontally at  its  centre  by  a  fine  point,  fig.  224.      When  a 
stick  of    sealing   wax,  or   a  glass  tube,  is  excited,  and  then 

From  what  is  the  term  electricity  derived  1  What  is  electrical  attrac- 
tion 7  What  are  electrics  1  What  are  non-electrics  1  What  are  the  prin- 
cipal electrics  1  What  is  meant  by  electrical  repulsion  1  What  is  an 
electroscope  1 


304 


ELECTRICITY. 


Fig.  225. 


presented  to  one  of  these  balls,  Fig.  234. 

the  motion  of  the  needle  on  its 
pivot  will  indicate  the  electri- 
cal  influence. 

902.  If  an  excited  substance 
be  brought  near  a  ball  made 
of  pith,  or  cork,  suspended  by  a 
silk  thread,  the  ball  will,  in 
the  first  place,  approach  the 
electric,  as  at  0,  fig.  225,  indi- 
cating an  attraction  towards  it, 
and  if  the  position  of  the  elec* 
trie  will  allow,  the  ball  will 
come    into    contact   with  the 
electric,  and  adhere  to  it  for  a 
short  time,  and  will  then  recede 
from  it,  showing  that  it  is  re- 

pelled,  as  at  b.  If  now  the  ball  which  had  touched  the  elec- 
tric, be  brought  near  another  ball,  which  has  had  no  commu- 
nication with  an  excited  substance,  these  two  balls  will  attract 
each  other,  and  come  into  contact ;  after  which  they  will  re- 
pel each  other,  as  in  the  former  case. 

903.  It  appears,  therefore,  that  the  excited  body,  as  the 
stick  of  sealing  wax,  imparts  a  portion  of  its  electricity  to  the 
ball,  and  that  when  the  ball  is  also  electrified,  a  mutual  re- 
pulsion then  takes  place  between  them.      Afterwards,  the 
ball,  being  electrified  by  contact  with  the  electric,  when 
brought  near  another  ball  not  electrified,  transfers  a  part  of 
its  electrical  influence  to  that,  after  which  these  two  balls  re- 
pel each  other,  as  in  the  former  instance. 

904.  Thus,  when  one  substance  has  a  greater  or  less  quan- 
tity of  electricity  than  another,  it  will  attract  the  other  sub- 
stance, and  when  they  are  in  contact  will  impart  to  it  a  por- 
tion of  this  superabundance ;  but  when  they  are  both  equally 
electrified,  both  having  more  or  less  than  their  natural  quan- 
tity of  electricity,  they  will  repel  each  other. 

905.  To  account  for  these  phenomena,  two  theories  have 
been  advanced,  one  by  Dr.  Franklin,  who  supposes  there  is 


When  do  two  electrified  bodies  attract,  and  when  do  they  repel  each 
other  I  How  will  two  bodies  act,  one  having  more,  and  the  other  less, 
than  the  natural  quantity  of  electricity,  when  brought  near  each  other? 
How  will  they  act  when  both  have  more  or  less  than  their  natural 
quantity  1 


ELECTRICITY. 

omy  one  electrical  fluid,  and  the  other  by  Du  Fay,  who  sup- 
poses  that  there  are  two  distinct  fluids. 

906.  Dr.  Franklin  supposed  that  all  terrestrial  substances 
were  pervaded  with  the  electrical  fluid,  and  that  by  exciting 
an  electric,  the  equilibrium  of  this  fluid  was  destroyed,  so 
that  one  part  of  the  excited  body  contained  more  than  its 
natural  quantity  of  electricity,  and  the  other  part  less.     If  in 
this  state  a  conductor  of  electricity,  as  a  piece  of  metal,  be 
brought  near  the  excited  part,  the  accumulated  electricity 
would  be  imparted  to  it,  and  then  this  conductor  would  re- 
ceive more  than  its  natural  quantity  of  the  electric  fluid. 
This  he  called  positive  electricity.     But  if  a  conductor  be 
connected  with  that  part  which  has  less  than  its  ordinary 
share  of  the  fluid,  then  the  conductor  parts  with  a  share  of 
its  own,  and  therefore  will  then  contain  less  than  its  natural 
quantity.     This  he  called  negative  electricity.     When  one 
body  positively,  and  another  negatively  electrified,  are  con- 
nected by  a  conducting  substance,  the  fluid  rushes  from  the 
positive  to  the  negative  body,  and  the  equilibrium   is   re- 
stored.    Thus,  bodies  which  are  said  to  be  positively  electri- 
fied, contain  more  than  their  natural  quantity  of  electricity, 
while  those  which  are  negatively  electrified  contain  less  than 
their  natural  quantity. 

907.  The  other  theory  is  explained  thus.     When  a  piece 
of  glass  is  excited  and  made  to  touch  a  pith  ball,  as  above 
stated,  then  that  ball  will  attract  another  ball,  after  which 
they  will  mutually  repel  each  other,  and  the  same  will  hap- 
pen if  a  piece  of  sealing  wax  be  used  instead  of  the  glass. 
But  if  a  piece  of  excited  glass,  and  another  of  wax,  be  made 
to  touch  two  separate  balls,  they  will  attract  each  other  ;  that 
is,  the  ball  which  received  its  electricity  from  the  wax  will 
attract  that  which  received  its  electricity  from  the  glass,  and 
will  be  attracted  by  it.     Hence  Du  Fay  concludes  that  elec- 
tricity consists  of  two  distinct  fluids,  which  exist  together  in 
all  bodies— that  they  have  a  mutual  attraction  for  each  other 
— that  they  are  separated  by  the  excitation  of  electrics,  and 
that  when  thus  separated,  and  transferred  to  non-electrics, 
as  to  the  pith  baHs,  their  mutual  attraction  causes  the  balls 
to  rush  towards  each  other.     These  two  principles  he  called 

Explain  Dr.  Franklin's  theory  of  electricity.  What  is  meant  by 
positive,  and  what  by  negative  electricity  1  What  is  the  consequence, 
when  a  positive  and  a  negative  body  are  connected  by  a  conductor  \ 
Explain  Du  Fay's  theoty.  When  two  balls  are  electrified,  one  with 
glass,  and  the  other  with  wax,  will  they  attract  or  repel  each  other  ? 

2C* 


, 


306  ELECTRICITY. 

vitreous  and  resinous  electricity.  The  vitreous  being  ob- 
tained from  glass,  and  the  resinous  from  wax  and  other  re- 
sinous substances. 

908.  Dr.  Franklin's  theory  is  by  far  the  most  simple,  and 
will  account  for  most  of  the  electrical  phenomena  equally 
well  with  that  of  Du  Fay,  and  therefore  has  been  adopted 
by  the  most  able  and  recent  electricians. 

909.  It  is  found  that  some  substances  conduct  the  electrio 
fluid  from  a  positive  to  a  negative  surface  with  great  facility, 
while  others  conduct  it  with  difficulty,  and  others  not  at  all. 
Substances  of  the  first  kind  are  called  conductors,  and  those 
of  the  last  non-conductors.     The  electrics,  or  such  substances 
as,  being  excited,  communicate  electricity,  are  all  non-con- 
ductors, while  the  non-electrics,  or  such  substances  as  do  not 
communicate  electricity  on  being  merely  excited,  are  con- 
ductors.    The  conductors  are  the  metals,  charcoal,  water, 
and  other  fluids,  except  the  oils ;  also,  smoke,  steam,  ice,  and 
snow.     The  best  conductors  are  gold,  silver,  platina,  brass, 
and  iron. 

The  electrics,  or  non-conductors,  are  glass,  amber,  sulphur, 
resin,  wax,  silk,  most  hard  stones,  and  the  furs  of  some  ani- 
mals. 

910.  A  body  is  said  to  be  insulated,  when  it  is  supported 
or  surrounded  by  an  electric.      Thus,  a  stool  standing  on 
glass  legs,  is  insulated,  and  a  plate  of  metal  laid  on  a  plate 
of  glass,  is  insulated. 

911.  When  large  quantities  of  the  electric  fluid  are  want- 
ed for  experiment,  or  for  other  purposes,  it  is  procured  by  an 
electrical  machine.     These  machines  are  of  various  forms, 
but  all  consist  of  an  electric  substance  of  considerable  di- 
mensions ;  the  rubber  by  which  this  is  excited  ;    the  prime 
conductor,  on  which  the  electric  matter  is  accumulated;  the 
insulator,  which  prevents  the  fluid  from  escaping;  and  ma- 
chinery, by  which  the  electric  is  set  in  motion. 

912.  Fig.  226  represents  such  a  machine,  of  which  A  is 
the  electric,  being  a  cylinder  of  glass;  B  the  prime  con- 
ductor ;  R  the  rubber  or  cushion,  and  C  a  chain  connecting- 
the  rubber  with  the  ground.     The  prime  conductor  is  sup 

What  are  the  two  electricities  called  1  From  what  substances  are  the 
two  electricities  obtained  1  What  are  conductors  1  What  are  non-con- 
ductors 1  What  substances  are  conductors  1  What  substances  are  the 
best  conductors'?  What  substances  are  electrics,  or  non-conductors  1 
When  is  a  body  said  to  be  insulated  7  What  are  the  several  parts  of 
£n  electrical  machine  1 


\ 


ELECTRICITY. 
Fig.  225. 


307 


jv)j;ed  by  a  standard  of  glass.  Sometimes,  also,  the  pillars 
which  support  the  axis  of  the  cylinder,  and  that  to  which  the 
cushion  is  attached,  are  made  of  the  same  material.  The 
prime  conductor  has  several  wires  inserted  into  its  side,  or 
end,  which  are  pointed,  and  stand  with  the  points  near  the 
cylinder.  They  receive  the  electric  fluid  from  the  glass, 
and  convey  it  to  the  conductor.  The  conductor  is  commonly 
made  of  sheet  brass,  there  being  no  advantage  in  having  it 
solid,  as  the  electric  fluid  is  always  confined  entirely  to  the 
surface.  Even  paper,  covered  with  gold  leaf,  is  as  effective 
in  this  respect,  as  though  the  whole  was  of  solid  gold.  The 
cushion  is  attached  to  a  standard,  which  is  furnished  with  a 
thumb  screw,  so  that  its  pressure  on  the  cylinder  can  be  in- 
creased or  diminished.  The  cushion  is  made  of  leather, 
stuffed,  and  at  its  upper  edge  there  is  attached  a  flap  of  silk, 
F,  by  which  a  greater  surface  of  the  glass  is  covered,  and  the 
electric  fluid  thus  prevented,  in  some  degree,  from  escaping. 
The  efficacy  of  the  rubber  in  producing  the  electric  excita- 
tion is  much  increased  by  spreading  on  it  a  small  quantity 
of  an  amalgam  of  tin  and  mercury,  mixed  with  a  little  lard, 
or  other  unctuous  substance. 

What  is  the  use  of  the  pointed  wires  in  the  prime  conductor  1  How 
is  if,  accounted  for,  that  a  mere  surface  of  metal  will  contain  as  much 
electric  fluid  as  though  it  were  solid  1  When  a  piece  of  glass,  or  sealing 
wax,  is  excited,  by  rubbing  it  with  the  hand,  or  a  piece  of  silk,  whence 
comes  the  electricity "? 


308  ELECTRICITY. 

913.  The  manner  in  which  this  machine  acts,  may  be  in- 
ferred from  what  has  already  been  said,  for  when  a  stick  of 
sealing  wax,  or  a  glass  tube,  is  rubbed  with  the  hand,  or  a 
piece  of  silk,  the  electric  fluid  is  accumulated  on  the  excited 
substance,  and  therefore  must  be  transferred  from  the  hand, 
or  silk,  to  the  electric.      In   the  same  manner,  when  the 
cylinder  is  made  to  revolve,  the  electric  matter,  in  conse- 
quence of  the  friction,  leaves  the  cushion,  and  is  accumulated 
on  the  glass  cylinder,  that  is,  the  cushion  becomes  nega- 
tively, and  the  glass  positively  electrified.     The  fluid,  being 
thus  excited,  is  prevented  from  escaping  by  the  silk  flap,  until 
it  comes  to  the  vicinity  of  the  metallic  points,  by  which  it  is 
conveyed  to  the  prime  conductor.     But  if  the  cushion  is  in- 
sulated, the  quantity  of  electricity  obtained  will   soon  have 
reached  its  limit,  for  when  its  natural  quantity  has  been 
transferred  to  the  glass,  no  more  can  be  obtained.     It  is  then 
necessary  to  make  the  cushion  communicate  with  the  ground, 
which  is  done  by  laying  the  chain  on  the  floor,  or  table, 
when  more  of  the  fluid  will  be  accumulated,  by  further  ex- 
citation,  the  ground  being  the  inexhaustible  source  of  the 
electric  fluid. 

914.  If  a  person  who  is  insulated  takes  the  chain  in  his 
hand,  the  electric  fluid  will  be  drawn  from  him,  along  the 
chain,  to  the  cushion,  and  from  the  cushion  will  be  transfer- 
red to  the  prime  conductor,  and  thus  the  person  will  become 
negatively  electrified.     If,  then,  another  person,  standing  on 
the  floor,  hold  his  knuckle  near  him  who  is  insulated,  a 
spark  of  electric  fire  will  pass  between  them,  with  a  crack- 
ling noise,  and  the  equilibrium  will  be  restored  ;  that  is,  the 
electric  fluid  will  pass  from  him  who  stands  on  the  floor,  to 
him  who  stands  on  the  stool.     But  if  the  insulated  person 
takes  hold  of  a  chain,  connected  with  the  prime  conductor, 
he  may  be  considered  as  forming  a  part  of  the  conductor,  and 
therefore  the  electric  fluid  will  be  accumulated  all  over  his 
surface,  and  he  will  be  positively  electrified,  or  will  obtain 
more  than  his  natural  quantity  of  electricity.     If  now  a  per- 
son standing  on  the  floor  touch  this  person,  he  will  receive  a 

When  the  cushion  is  insulated,  why  is  there  a  limited  quantity  of 
electric  matter  to  be  obtained  from  it  1  What  is  then  necessary,  that 
more  electric  matter  may  be  obtained  from  the  cushion  ?  If  an  insulated 
person  takes  the  chain,  connected  with  the  cushion,  in  his  hand,  what 
change  will  be  produced  in  his  natural  quantity  of  electricity  1  If  the 
insulated  person  takes  hold  of  the  chain  connected  with  the  prime  con- 
ductor, and  the  machine  be  worked,  what  then  will  be  the  change  pro- 
duced in  his  electrical  state? 


ELECTRICITY.  309 

spark  of  electrical  fire  from  him,  and  the  equilibrium  will 
again  be  restored. 

915.  If  two  persons  stand  on  two  insulated  stools,  or  if 
they  both  stand  on  a  plate  of  glass,  or  a  cake  of  wax,  the 
one  person  being  connected  by  the  chain  with  the  prime  con- 
ductor, and  the  other  with  the  cushion,  then,  after  working 
the  machine,  if  they  touch  each  other,  a  much   stronger 
shock  will  be  felt  than  in  either  of  the  other  cases,  because 
the  difference  between  their  electrical  states  will  be  greater, 
the  one  having  more  and  the  other  less  than  his  natural 
quantity  of  electricity.     But  if  the  two  insulated  persons  both 
take  hold  of  the  chain  connected  with  the  prime  conductor, 
or  with  that  connected  with  the  cushion,  no  spark  will  pass 
between  them,  on  touching  each  other,  because  they  will 
then  both  be  in  the  same  electrical  state. 

916.  We  have  seen,  fig.  224,  that  the  pith  ball  is  first  at- 
tracted and  then  repelled,  by  the  excited  electric,  and  that  the 
ball  so  repelled  will  attract,  or  be  attracted  by  other  sub- 
stances in  its  vicinity,  in  consequence  of  having   received 
from  the  excited  body  more  than   its  ordinary  quantity  of 
electricity. 

These  alternate  movements  areamus-  Fig.  227.^ 
ingly  exhibited,  by  placing  some  small 
light  bodies,  such  as  the  figures  of  men 
and  women,  made  of  pith,  or  paper,  be- 
tween two  metallic  plates,  the  one  placed 
over  the  other,  as  in  fig.  227,  the  upper 
plate  communicating  with  the  prime  con- 
ductor, and  the  other  with  the  ground. 
When  the  electricity  is  communicated 
to  the  upper  plate,  the  little  figures, 
being  attracted  by  the  electricity,  will 
jump  up  and  strike  their  heads  against 
it,  and  having  received  a  portion  of  the 
fluid,  are  instantly  repelled,  and  again 
attracted  by  the  lower  plate,  to  which 
they  impart  their  electricity,  and  then  are  again  attracted, 
arid  so  fetch  and  carry  the  electric  fluid  from  one  to  the 
other,  as  long  as  the  upper  plate  contains  more  than  the 

If  two  insulated  persons  take  hold  of  the  two  chains,  one  connected 
with  the  prime  conductor,  and  the  other  with  the  cushion,  what  changes 
will  be  produced  1  If  they  both  take  hold  of  the  same  chain,  what  wul 
be  the  effect  7  Explain  the  reason  why  the  little  images  dance  between 
the  two  metallic  plates,  fig.  227. 


310  ELECTRICITY. 

lower  one.  In  the  same  manner,  a  tumbler,  if  electrified  on 
the  inside,  and  placed  over  light  substances,  as  pith  balls,  will 
cause  them  to  dance  for  a  considerable  time. 

917.  This  alternate  attraction  and  repulsion,  by  moveable 
conductors,  is  also  pleasingly  illustrated  with  a  ball,  suspend- 
ed by  a  silk  string  between  two  bells  of  brass,  fig.  228,  one 
of  the  bells  being  electrified,  and  the  Fig.  228. 
other  communicating  with  the  ground. 
The  alternate  attraction  and  repul- 
sion, moves  the  ball  from  one  bell  to    

the  other,  and  thus  produces  a  con- 
tinual ringing.  In  all  these  cases, 
the  phenomena  will  be  the  same, 
whether  the  electricity  be  positive 
or  negative;  for  two  bodies,  being 
both  positively  or  negatively  electri- 
fied, repel  each  other,  but  if  one  be 
electrified  positively,  and  the  other 
negatively,  or  not  at  all,  they  attract 
each  other. 

Thus,  a  small  figure,  in  the  human  shape,  with  the  head 
covered  with  hair,  when  electrified,  either  positively  or  ne- 
gatively, will  exhibit  an  appearance  of  the  utmost  terror, 
each  hair  standing  erect,  and  diverging  from  the  other,  in 
consequence  of  mutual  repulsion.  A  person  standing  on  an 
insulated  stool,  and  highly  electrified,  will  exhibit  the  same 
appearance.  In  cold,  dry  weather,  the  friction  produced 
by  combing  a  person's  hair,  will  cause  a  less  degree  of  the 
same  effect.  In  either  case,  the  hair  will  collapse,  or  shrink 
to  its  natural  state,  on  carrying  a  needle  near  it,  because  this 
conducts  away  the  electric  fluid.  Instruments  designed  to 
measure  the  intensity  of  electric  action,  are  called  electro- 
meters. 

918.  Such  an  instrument  is  represented  by  fig.  229.  It 
consists  of  a  slender  rod  of  light  wood,  a,  terminated  by  a 
pith  ball,  which  serves  as  an  index.  This  is  suspended  at 
the  upper  part  of  the  wooden  stem  b,  so  as  to  play  easily 
backwards  and  forwards.  The  ivory  semicircle  c,  is  affixed 
to  the  stem,  having  its  centre  coinciding  with  the  axis  of  mo- 
Explain  fig.  228.  Does  it  make  any  difference  in  respect  to  the  mo- 
tion of  the  images,  or  of  the  ball  between  the  bells,  whether  the  electri- 
city be  positive  or  negative  1  When  a  person  is  highly  electrified,  why 
does  he  exhibit  an  appearance  of  the  utmost  terror "?  What  is  an  eleo- 
trometer  ? 


ELECTRICITY. 


311 


tion  of  the  rod,  so  as  to  measure  the  angle  of      Fig.  229. 
deviation  from  the  perpendicular,  which  the 
repulsion  of  the  ball  from  the  stem  produces 
in  the  index. 

When  this  instrument  is  used,  the  lower 
end  of  the  stem  is  set  into  an  aperture  in  the 
prime  conductor,  and  the  intensity  of  the  elec- 
tric action  is  indicated  by  the  number  of  de- 
grees the  index  is  repelled  from  the  perpen- 
dicular. 

The  passage  of  the  electric  fluid  through 
a  perfect  conductor  is  never  attended  with 
light,  or  the  crackling  noise,  which  is  heard 
when  it  is  transmitted  through  the  air,  or  along  the  surface 
of  an  electric. 

919.  Several  curious  experiments  illustrate  this  principle 
for  if  fragments  of  tin  foil,  or  other  metal,  be  pasted  on  a 
piece  of  glass,  so  neqr  each  other  that  the  electric  fluid  can 
pass  between  them/  the  whole  line  thus  formed  with  the 
pieces  of  metal,  will  be  illuminated  by  the  passage  of  the 
electricity  from  one  to  the  other. 
Fig.  230. 


^000000  Oo 

' 


920.  In  this  manner,  figures  or  words  may  be  formed,  as 
in  fig.  230,  which,  by  connecting  one  of  its  ends  with  the 
prime  conductor,  and  the  other  with  the  ground,  will,  when 
the  electric  fluid  is  passed  through  the  whole,  in  the  dark, 
appear  one  continuous  and  vivid  line  of  fire. 

921.  Electrical  light  seems  not  to  differ,  in  any  respect, 
from  the  light  of  the  sun,  or  of  a  burning  lamp.     Dr.  Wol- 
laston  observed,  that  when  this  light  was  seen  through  a 
prism,  the  ordinary  colours  arising  from  the  decomposition 
of  light  were  obvious. 

Describe  that  represented  in  fig.  229,  together  with  the  mode  of  using 
tf  When  the  electric  fluid  passes  along  a  perfect  conductor,  is  it  at- 
tended with  light  and  noise,  or  not"?  When  it  passes  along  an  electric, 
or  through  the  air,  what  phenomena  does  it  exhibit  7  Describe  the  ex- 
periment, fig.  230,  intended  to  illustrate  this  principle.  What  is  the 
appearance  of  electrical  light  through  a  prism! 


312  ELECTRICITY. 

922.  Tne  brilliancy  of  electrical  sparks  is  proportional  to 
the  conducting  power  of  the  bodies  between  which  it  passe?. 
When  an  imperfect  conductor,  such  as  a  piece  of  wood,  is 
employed,  the  electric  light  appears  in  faint,  red  streams, 
while,  if  passed  between  two  pointed  metals,  its  colour  is  of 
a  more  brilliant  red.      Its  colour  also  differs,  according  to 
the  kind  of  substance  from,  or  to  which,  it  passes,  or  it  is  de- 
pendant on  peculiar  circumstances.      Thus,  if  the  electric 
fluid  passes  between  two  polished  metallic  surfaces,  its  colour 
is  nearly  white  ;  but  if  the  spark  is  received  by  the  finger 
from  such  a  surface,  it  will  be  violet.     The  sparks  are  green, 
when  taken  by  the  finger  from  a  surface  of  silvered  leather ; 
yelloiv,  when  taken  from  finely  powdered  charcoal ;    and 
purple,  when  taken  from  the  greater  number  of  imperfect 
conductors. 

923.  When  the  electric  fluid  is  discharged  from  a  point, 
it  is  always  accompanied  by  a  current  of  air,  whether  the 
electricity  be  positive  or  negative.     The  reason  of  this  ap- 
pears to  be,  that  the  instant  a  particle  of  air  becomes  electri- 
fied, it  repels,  and  is  repelled,  by  the  point  from  which  it  re- 
ceived the  electricity. 

924.  Several  curious  little  experiments  are  made  on  this 
principle.     Thus,  let  two  cross  wires,  as  in  fig.  231,  be  sus- 
pended on  a  pivot,  each  having  its  point          Fig.  231. 
bent  in  a  contrary  direction,  and  electri- 
fied by  being  placed  on  the  prime  con- 
ductor of  a  machine.      These  points,  so 

long  as  the  machine  is  in  action,  will  give 
off  streams  of  electricity,  and  as  the  parti- 
cles of  air  repel  the  points  by  which  they 
are  electrified,  the  little  machine  will  turn 
round  rapidly,  in  the  direction  contrary  to 
that  of  the  stream  of  electricity.  Perhaps,  also,  the  reaction 
of  the  atmosphere  against  the  current  of  air  given  off  by  the 
points,  assists  in  giving  it  motion. 

925.  When  one  part  or  side  of  an  electric  is  positively,  the 
other  part  or  side  is  negatively  electrified.     Thus,  if  a  plate 
of  glass  be  positively  electrified  on  one  side,  it  will  be  nega- 
tively electrified  on  the  other,  and  if  the  inside  of  a  glass  ves- 
sel be  positive,  the  outside  will  be  negative. 

What  is  said  concerning  the  different  colours  of  electrical  light,  when 
passing  between  surfaces  of  different  kinds'?  Describe  fig.  231,  and 
explain  the  principle  on  which  its  motion  depends.  Suppose  one  part 
or  side  of  an  electric  is  positive,  what  will  be  the  e'ectrical  state  of  the 
other  side  or  part  1 


ELECTRICITY.  313 

£26.  Advantage  of  this  circumstance  is  taken,  in  the  con- 
jjtructiofi  of  electrical  jars,  called,  from  the  place  where  they 
were  first  made,  Leyden  vials. 

The  most  common  form  of  this  jar  is  repre-  Fig.  232. 
sented  by  fig.  232.  It  consists  of  a  glass  ves- 
sel, coated  on  both  sides,  up  to  a,  with  tin  foil; 
the  upper  part  being  left  naked,  so  as  to  pre- 
vent a  spontaneous  discharge,  or  the  passage 
of  the  electric  fluid  from  one  coating  to  the 
other.  A  metallic  rod,  rising  two  or  three 
inches  above  the  jar,  and  terminating  at  the 
top  with  a  brass  ball,  which  is  called  the 
knob  of  the  jar,  is  made  to  descend  through 
the  cover,  till  it  touches  the  interior  coating. 
It  is  along  this  rod  that  the  charge  of  elec- 
tricity is  conveyed  to  the  inner  coating,  while 
the  outer  coating  is  made  to  communicate  with  the  ground. 

927.  When  a  chain  is  passed  from  the  prime  conductor  of 
an  electrical  machine  to  this  rod,  the  electricity  is  accumu- 
lated on  the  tin  foil  coating,  while  the  glass  above  the  tin 
foil  prevents  its  escape,  and  thus  the  jar  becomes  charged. 
By  connecting  together  a  sufficient  number  of  these  jars,  any 
quantity  of  the  electric  fluid  may  be  accumulated.     For  this 
purpose,  all   the  interior  coatings  of  the  jars  are  made  to 
communicate  with  each  other,  by  metallic  rods  passing  be- 
tween them,  and  finally  terminating  in  a  single  rod.     A 
similar  union  is  also  established,  by  connecting  the  external 
coats  with  each  other.     When  thus  arranged,  the  whole  se- 
ries may  be  charged,  as  if  they  formed  but  one  jar,  and  the 
whole  series  may  be  discharged  at  the  same  instant.     Such 
a  combination  of  jars  is  termed  an  electrical  battery. 

928.  For  the  purpose  of  making  a  direct  communication 
between  the  inner  and  outer  coating  of  a  single  jar,  or  bat- 
tery, by  which  a  discharge  is  effected,  an  instrument  called 
a  discharging  rod  is  employed.     It  consists  of  two  bent 
metallic  rods,  terminated  at  one  end  by  brass  balls,  and  at  the 
other  end  connected  by  a  joint.     This  joint  is  fixed  to  the  end 
of  a  glass  handle,  and  the  rods  being  moveable  at  the  joint, 
the  balls  can  be  separated,  or  brought  near  each  other,  as 

What  part  of  the  electrical  apparatus  is  constructed  on  this  principle  1 
How  is  the  Leyden  vial  constructed  1  Why  is  not  the  whole  surface  of 
the  vial  covered  with  the  tin  foil  1  How  is  the  Leyden  vial  charged  7 
In  what  manner  may  a  number  of  these  vials  be  charged  1  What  is  an 
electrical  battery  1 

27 


314  ELECTRICITY. 

occasion  requires,  When  opened  to  a  proper  distance,  one 
ball  ia  made  to  touch  the  tin  foil  on  the  outside  of  the  jar,  and 
then  the  other  is  brought  in  Fig.  233. 

contact  with  the  knob  of  the  jar,  ^^-®  O 

as  seen  in  fig.  233.  In  this 
manner  a  discharge  is  effected, 
or  an  equilibrium  produced  be- 
tween the  positive  and  negative 
sides  of  the  jar. 

When  it  is  desired  to  pass 
the  charge  through  any  sub- 
stance for  experiment,  then  an 
electrical  circuit  must  be  estab- 
lished, of  which  the  substance  to  be  experimented  on  must 
form  a  part.  That  is,  the  substance  must  be  placed  between 
the  ends  of  two  metallic  conductors,  one  of  which  communi- 
cates with  the  positive,  and  the  other  with  the  negative  side 
of  the  jar,  or  battery. 

929.  When  a  person  takes  the  electrical  shock  in  the 
usual  manner,  he  merely  takes  hold  of  the  chain  connected 
with   the  outside  coating,  and  the  battery  being  charged, 
touches  the  knob  with  his  finger,  or  with  a  metallic  rod. 
On  making  this  circuit,  the  fluid  passes  through  the  person 
from  the  positive  to  the  negative  side. 

930.  Any  number  of  persons  may  receive  the  electrical 
shock,  by  taking  hold  of  each  other's  hands,  the  first  person 
touching  the  knob,  while  the  last  takes  hold  of  a  chain  con- 
nected with  the  external  coating.     In  this  manner,  hundreds, 
or  perhaps  thousands  of  persons,  will  feel  the  shock  at  the 
same  instant,  there  being  no  perceptible  interval  in  the  time 
when  the  first  and  the  last  person  in  the  circle   feels  the 
sensation  excited  by  the  passage  of  the  electric  fluid. 

931.  The  atmosphere  always  contains  more  or  less  elec- 
tricity, which  is  sometimes  positive,  and  at  others  negative. 
It  is,  however,  most  commonly  positive,  and  always  so  when 
the  sky  is  clear,  or  free  from  clouds  or  fogs.      It  is  always 
stronger  in  winter  than  in  summer,  and  during  the  day  than 
during  the  night.     It  is  also  stronger  at  some  hours  of  the 


ducec 

fluid 

two  sides  of  the  battery  1  Suppose  the  battery  is  charged,  what  must  a 

person  do  to  take  the  shock  1    What  circumstance  is  related,  which 

shows  the  surprising  velocity  with  which  electricity  is  transmitted  1 

Ts  the  electricity  of  the  atmosphere  positive  or  negative  7 


ELECTRICITY.  315 

day  than  at  others ;  being  strongest  about  9  o'clock  in  the 
morning,  and  weakest  about  the  middle  of  the  afternoon. 
These  different  electrical  states  are  ascertained  by  means  of 
tong  metallic  wires  extending  from  one  building  to  another, 
ind  connected  with  electrometers. 

932.  It  was  proved  by  Dr.  Franklin,  that  the  electric 
fluid  and  lightning  are  the  same  substance,  and  this  identity 
aas  been  confirmed  by  subsequent  writers  on  the  subject. 

If  the  properties  and  phenomena  of  lightning  be  com- 
oared  with  those  of  electricity,  it  will  be  found  that  they  dif- 
jer  only  in  respect  to  degree.  Thus,  lightning  passes  in  ir- 
regular lines  through  the  air ;  the  discharge  of  an  elec- 
trical battery  has  the  same  appearance.  Lightning  strikes 
the  highest  pointed  objects — takes  in  its  course  the  best  con- 
ductors— sets  fire  to  non-conductors,  or  rends  them  in  pieces 
— arid  destroys  animal  life ;  all  of  which  phenomena  are 
caused  by  the  electric  fluid. 

983.  Buildings  may  be  secured  from  the  effects  of  light- 
ning. Ly  fixing  to  them  a  metallic  rod,  which  is  elevated 
above  any  part  of  the  edifice  and  continued  to  the  moist 
ground,  or  to  the  nearest  water.  Copper,  for  this  purpose, 
is  better  ihan  iron,  not  only  because  it  is  less  liable  to  rust, 
but  because  it  is  a  belter  conductor  of  the  electric  fluid.  The 
upper  pan  of  the  rod  should  end  in  several  fine  points, 
which  must  be  covered  with  some  metal  not  liable  to  rust, 
such  as  gold,  piatina,  or  silver.  No  protection  is  afforded 
by  the  conductor  unless  it  is  continued  without  interruption 
from  the  top  to  the  oottom  of  the  building,  and  it  cannot  be 
relied  on  as  o>  protector,  unless  it  reaches  the  moist  earth,  or 
ends  in  water  connected,  with  the  earth.  Conductors  of  cop- 
per may  be  three  rourths  of  an  inch  in  diameter,  but  those  of 
iron  should  be  5tt  least  an  inch  in  diameter.  In  large  build- 
ings, complete  imrtection  requires  many  lightning  rods,  or 
that  they  should  be  elevated  10  a  height  above  the  building 
in  proportion  to  the  smailness  of  their  numbers,  for  modern 
experiments  have  proved  that  a  rod  only  protects  a  circle 
around  it,  the  radius  of  which  is  equal  to  twice  its  length 
above  the  building. 

At  what  times  does  the  atmosphere  contain  most  electricity  7  How  are 
the  different  electrical  states  of  the  atmosphere  ascertained  1  Who  first 
discovered  that  electricity  and  lightning  are  the  same  7  What  phenomena 
are  mentioned  which  belong  in  common  to  electricity  and  lightning  1 
How  may  buildings  be  protected  from  the  effects  of  lightning  1  Which 
is  the  best  conductor,  iron  or  copper  1  What  circumstances  are  neces- 
sary, that  the  rod  may  be  relied  on  as  a  protector  7 


316  MAGNETISM. 

934.  Some  fishes  have  the  power  of  giving  electrical 
shocks,  the  effects  of  which  are  the  same  as  those  obtained 
by  the  friction  of  an  electric.     The  best  known  of  these  are 
the  Torpedo,  the  Gymnotus  electricus,  and  the  Silurus  elec- 
tricus. 

935.  The  torpedo,  when  touched  with  both  hands  at  the 
same  time,  the  one  hand  on  the  under,  and  the  other  on  the 
upper  surface,  will  give  a  shock  like  that  of  the  Leyden 
vial ;  which  shows  that  the  upper  and  under  surfaces  of  the 
electric  organs  are  in  the  positive  and  negative  state,  like  the 
inner  and  outer  surraces  of  the  electrical  jar. 

936.  The  gymnotus  electricus,  or  electrical  eel,  possesses 
all  the  electrical  powers  of  the  torpedo,  but  in  a  much  higher 
degree.     When  small  fish  are  placed  in  the  water  with  this 
animal,  they  are  generally  stunned,  and  sometimes  killed, 
by  his  electrical  shock,  after  which  he  eats  them  if  hungry. 
The  strongest  shock  of  the  gymnotus  will  pass  a  short  dis- 
tance through  the  air,  or  across  the  surface  of  an  electric, 
from  one  conductor  to  another,  and  then  there  can  be  per- 
ceived a  small  but  vivid  spark  of  electrical  fire  ;  particularly 
if  the  experiment  be  made  in  the  dark. 

MAGNETISM. 

937.  The  native  Magnet,  or  Loadstone,  is  an  ore  of  iron, 
which  is  found  in  various  parts  of  the  world.     Its  colour  is 
iron  black ;  its  specific  gravity  from  4  to  5,  and  it  is  some- 
times found  in  crystals.     This  substance,  without  any  pre- 
paration, attracts  iron  and  steel,  and  when  suspended  by  a 
string,  will   turn  one  of  its  sides  towards  the  north,  and 
another  towards  the  south. 

938.  It  appears  that  an  examination  of  the  properties  of 
this  species  of  iron  ore,  led  to  the  important  discovery  of  the 
magnetic  needle,  and  subsequently  laid  the  foundation  for  the 
science  of  Magnetism ;  though  at  the  present  day  magnets  are 
made  without  this  article. 

939.  The  whole  science  of  magnetism  is  founded  on  the 
fact,  that  pieces  of  iron  or  steel,  after  being  treated  in  a  certain 
manner,  and  then  suspended,  will  constantly  turn  one  of  their 
ends  towards  the  north,  and  consequently  the  other  towards 

What  animals  have  the  power  of  giving  electrical  shocks  1  Is  this 
electricity  supposed  to  differ  from  that  obtained  by  art  1  How  must  the 
hands  be  applied,  to  take  the  electrical  shock  of  these  animals?  What 
is  the  native  magnet,  or  loadstone"?  What  are  the  properties  of  the 
loadstone  ?  On  what  is  the  whole  subject  of  magnetism  founded  1 


MAGNETISM.  317 

.he  south.  The  same  property  has  been  more  recently- 
proved  to  belong  to  the  metals  mckel  and  cobalt,  though 
with  much  less  intensity. 

940.  The  poles  of  a  magnet  are  those  parts  which  possess 
the  greatest  power,  or  in  which  the  magnetic  virtue  seems 
to  be  concentrated.     One  of  the  poles  points  north,  and  the 
other  south.      The  magnetic  meridian  is  a  vertical  circle 
in  the  heavens,  which  intersects  the  horizon  at  the  points  to 
which  the  magnetic  needle,  when  at  rest,  directs  itself. 

941.  The  axis  of  a  magnet,  is  a  right  line  which  passes 
from  one  of  its  poles  to  the  other. 

942.  The  equator  of  a  magnet,  is  a  line  perpendicular  to 
its  axis,  and  is  at  the  centre  between  the  two  poles. 

943.  The  leading  properties  of  the  magnet  are 'the  fol- 
lowing.    It  attracts  iron  and  steel,  and  when  suspended  so 
as  to  move  freely,  it  arranges  itself  so  as  to  point  north  and 
south  :  this  is  called  the  polarity  of  the  magnet.     When  the 
south,  pole  of  one  magnet  is  presented  to  the  north  pole  of 
another,  they  will  attract  each  other :  this  is  called  magnetic 
attraction.     But  if  the  two  north  or  two  south  poles  be 
brought  together,  they  will  repel  each  other,  and  this  is 
called  magnetic  repulsion.     When  a  magnet  is  left  to  move 
freely,  it  does  not  lie  in  a  horizontal  direction,  but  one  pole 
inclines  downwards,  and  consequently  the  other  is  elevated 
above  the  line  of  the  horizon.     This  is  called  the  dipping, 
or  inclination  of  the  magnetic  needle.     Any  magnet  is  ca- 
pable of  communicating  its  own  properties  to  iron  or  steel, 
and  this,  again,  will  impart  its  magnetic  virtue  to  another 
piece  of  steel,  and  so  on  indefinitely. 

944.  If  a  piece  of  iron  or  steel  be  brought  near  one  of 
the  poles  of  a  magnet,  they  will  attract  each  other,  and  if 
suffered  to  come  into  contact,  will  adhere  so  as  to  require 
force  to  separate  them.     This  attraction  is  mutual ;  for  the 
iron  attracts  the  magnet  with  the  same  force  that  the  mag- 
net attracts  the  iron.     This  may  be  proved,  by  placing  the 
iron  and  magnet  on  pieces  of  wood  floating  on  water,  when 
they  will  be  seen  to  approach  each  other  mutually. 

What  other  metals  besides  iron  possess  the  magnetic  property  1 
What  are  the  poles  of  a  magnet  1  What  is  the  axis  of  a  magnet  1  What 
is  the  equator  of  a  magnet  1  What  is  meant  by  the  polarity  of  a  mag- 
net 7  When  do  two  magnets  attract,  and  when  repel  each  other"? 
What  is  understood  by  the  dipping  of  the  magnetic  needle  1  How  is  it 
nroved  that  the.  iron  attracts  the  magnet  with  the  same  force  that  the 
magnet  attracts  the  iron  1 

27* 


318  MAGNETISM. 

945.  The  force  of  magnetic  attraction  varies  with  the  dip- 
tance  in  the  same  ratio  as  the  force  of  gravity  j  the  attract- 
ing force  being  inversely  as  the  square  of  the  distance  be- 
tween the  magnet  and  the  iron. 

946.  The  magnetic  force  is  not  sensibly  affected  by  the 
interposition  of  any  substance  except  those  containing  iron, 
or  steel.     Thus,  if  two  magnets,  or  a  magnet  and  piece  of 
iron,  attract  each  other  with  a  certain  force,  this  force  will 
be  the  same,  if  a  plate  of  glass,  wood,  or  paper,  be  placed  be- 
tween them.      Neither  will  the  force  be  altered,  by  placing 
the  two  attracting  bodies  under  water,  or  in  the  exhausted 
receiver  of  an  air  pump.     This  proves  that  the  magnetic  in- 
fluence passes  equally  well  through  air,  glass,  wood,  paper, 
water,  and  a  vacuum, 

947.  Heat  weakens  the  attractive  power  of  the  magnet, 
and  a  white  heat  entirely  destroys  it.    Electricity  will  change 
the  poles  of  the  magnetic  needle,  and  the  explosion  of  a 
small  quantity  of  gun-powder  on  one  of  the  poles,  will  have 
the  same  effect. 

948.  The  attractive  power  of  the  magnet  may  be  increased 
by  permitting  a  piece  of  steel  to  adhere  to  it,  and  then  sus- 
pending to  the  steel  a  little  additional  weight  every  day,  for 
it  will  sustain,  to  a  certain  limit,  a  little  more  weight  on  one 
day  than  it  would  on  the  day  before. 

949.  Small  natural  magnets  will  sustain  more  than  large 
ones  in  proportion  to  their  weight.     It  is  rare  to  find  a  na- 
tural magnet,  weighing  20  or  30  grains,  which  will  lift  mose 
than  thirty  or  forty  times  its  own  weight.     But  a  minute 
piece  of  natural  magnet,  worn  by  Sir  Isaac  Newton,  in  a 
ring,  which  weighed  only  three  grains,  is  said  to  have  been 
capable  of  lifting  746  grains,  or  nearly  250  times  its  own 
weight. 

950.  The  magnetic  property  may  be  communicated  from 
the  loadstone,  or  artificial  magnet,  in  the  following  manner, 
it  being  understood  that  the  north  pole  of  one  of  the  mag- 
nets employed,  must  always  be  drawn  towards  the  south  pole 
of  the  new  magnet,  and  that  the  south  pole  of  the  other  mag- 
net employed,  is  to  be  drawn  in  the  contrary  direction.     The 

How  does  the  force  of  magnetic  attraction  vary  with  the  distance  ? 
Does  the  magnetic  force  vary  with  the  interposition  of  any  substance 
between  the  attracting  bodies  1  What  is  the  effect  of  heat  on  the  mag- 
net 7  What  is  the  effect  of  electricity,  or  the  explosion  of  g-un -powder 
on  it  1  How  may  the  power  of  a  magnet  be  increased  1  What  is  sai  j 
concerning  the  comparative  powers  of  great  and  small  magnets  7 


MAGNETISM.  319 

north  poles  of  magnetic  bars  are  usually  marked  with  a  line 
across  them,  so  as  to  distinguish  this  end  from  the  other. 

951.  Place  two  mag-  Fig.  234. 
netic  bars,  a  and  b,  fig. 

234,  so  that  the  north 
end  of  one  may  be  near- 
est the  south  end  of  the 
other,  and  at  such  a  dis- 
tance that  the  ends  of  the 
steel  bar  to  be  touched, 
may  rest  upon  them.  Having  thus  arranged  them,  as 
shown  in  the  figure,  take  the  two  magnetic  bars,  d  and  «, 
and  apply  the  south  end  of  e,  and  the  north  end  of  d,  to  the 
middle  of  the  bar  c,  elevating  their  ends  as  seen  in  the  figure. 
Next  separate  the  bars  e  and  d,  by  drawing  them  in  oppo- 
site directions  along  the  surface  of  c,  still  preserving  the  ele- 
vation of  their  ends  ;  then  removing  the  bars  d  and  e  to  the 
distance  of  a  foot  or  more  from  the  bar  c,  bring  their  north 
and  south  poles  into  contact,  and  then  having  again  placed 
them  on  the  middle  of  c,  draw  them  in  contrary  directions, 
as  before.  The  same  process  must  be  repeated  many  times 
on  each  side  of  the  bar  c,  when  it  will  be  found  to  have  ac 
quired  a  strong  and  permanent  magnetism. 

952.  If  a  bar  of  iron  be  placed,  for  a  long  period  of  time, 
in  a  north  and  south  direction,  or  in  a  perpendicular  posi- 
tion, it  will  often  acquire  a  strong  magnetic  power.     Old 
tongs,  pokers,  and  fire  shovels,  almost  always  possess  more 
or  less  magnetic  virtue,  and  the  same  is  found  to  be  the  case 
with  the  iron  window  bars  of  ancient  houses,  whenever  they 
have  happened  to  be  placed  in  the  direction  of  the  magnetic 
line. 

953.  A  magnetic  needle,  such  as  is  employed  in  the  mari- 
ner's and  surveyor's  compass,  may  be  made  by  fixing  a 
piece  of  steel  on  a  board,  and  then  drawing  two  magnets 
from  the  centre  towards  each  end,  as  directed  at  fig.  234. 
Some  magnetic  needles  in  time  lose  their  virtue,  and  require 
again  to  be  magnetized.     This  may  be  done  by  placing  the 
needle,  still  suspended  on  its  pivot,  between  the  opposite  poles 
of  two  magnetic  bars.     While  it  is  receiving  the  magnet- 
ism, it  wilf  be  agitated,  moving  backwards  and  forwards,  as 

Explain  fig.  234,  and  describe  the  mode  of  making  a  magnet.  In 
what  positions  do  bars  of  iron  become  magnetic  spontaneously  1  How 
may  a  needle  be  magnetized  without  removing  it  from  its  pivot  1 


320  MAGNETISM. 

though  it  were  animated,  but  when  it  has  become  perfectly 
magnetized,  it  will  remain  quiescent. 

954.  The  dip,  or  inclination  of  the  magnetic  needle,  is  its 
deviation  from  its  horizontal  position,  as  already  mentioned. 
A  piece  of  steel,  or  a  needle,  which  will  rest  on  its  centre, 
in  a  direction  p  .rallel  to  the  horizon,  before  it  is  magnet- 
ized, will  afterwards   incline  one  of  its  ends  towards  the 
earth.     This  property  of  the  magnetic  needle  was  discovered 
by  a  compass  maker,  who,  having  finished   his  needles  be- 
fore they  were  magnetized,  found  that  immediately  after- 
wards, their  north  ends  inclined  towards  the  earth,  so  that 
he  was  obliged  to  add  small  weights  to  their  south  poles,  in 
order  to  make  them  balance,  as  before. 

955.  The  dip  of  the  magnetic  needle  is  measured  by  a 
graduated   circle,  placed  in  the  vertical  position,  with  the 
needle  suspended  by  its  side.      Its  inclination  from  a  hori- 
zontal line  marked  across  the  face  of  this  circle,  is  the  mea- 
sure of  its  dip.    The  eircle,  as  usual,  is  divided  into  360  de- 
grees, and  these  into  minutes  and  seconds. 

956.  The  dip  of  the  needle  does  not  vary  materially  at  the 
same  place,  but  differs  in  different  latitudes,  increasing  as  it 
is  carried  towards  the  north,  and  diminishing  as  it  is  carried 
towards  the  south.     At  London,  the  dip  for  many  years  has 
varied  little  from  72  degrees.     In  the  latitude  of  80  degrees 
north,  the  dip,  according  to  the  observations  of  Capt.  Parry, 
was  88  degrees. 

957.  Although,  in  general  terms,  the  magnetic  needle  is 
said  to  point  north  and  south,  yet  this  is  very  seldom  strictly 
true,  there  being  a  variation  in  its  direction,  which  differs  in 
degree  at  different  times  and  places.     This  is  called  the  va- 
riation, or  declination,  of  the  magnetic  needle. 

958.  This  variation  is  determined  at  sea,  by  observing 
the  different  points  of  the  compass  at  which  the  sun  rises,  o*- 
sets,  and  comparing  them  with  the  true  points  of  the  sun's 
rising  or  setting,  according  to  astronomical  tables.     By  such 
observations  it  has  been  ascertained  that  the  magnetic  needle 
is  continually  declining  alternately  to  the  east  or  west  from  due 
north,  and  that  this  variation  differs  in  different  parts  of  the 

How  was  the  dip  of  the  magnetic  needle  first  discovered  1  In  what 
manner  is  the  dip  measured  1  What  circumstance  increases  or  dimi- 
nishes the  dip  of  the  needle  1  What  is  meant  by  the  declination  of  the 
magnetic  needle  1  How  is  this  variation  determined  7  What  has  been 
ascertained  concerning  the  variation  of  the  needle  at  different  time*. 
and  places  1 


GALVANISM. 

world  at  the  same  time,  and  at  the  same  place  at  different 
times. 

959.  In  1580,  the  needle  at  London  pointed  11  degrees 
15  minutes  east  of  north,  and  in  1657  it  pointed  due  north 
and  south,  so  that  it  moved  during  that  time  at  the  mean  rate 
of  about  9  minutes  of  a  degree  in  each  year,  towards  the 
north.     Since  1657,  according  to  observations  made  in  Eng- 
land, it  has  declined  gradually  towards  the  west,  so  that  in 
1803,  its  variation  west  of  north  was  24  degrees. 

960.  At  Hartford,  Connecticut,  in  latitude  about  41,  it  ap- 
pears from  a  record  of  its  variations,  that  since  the  year 
1824,  the  magnetic  needle  has  been  declining  towards  the 
west,  at  the  mean  rate  of  3  minutes  of  a  degree  annually, 
and  that  on  the  20th  of  July,  1829,  the  variation  was  6  de- 
grees 3  minutes  west  of  the  true  meridian. 

961.  The  cause  of  this  annual  variation  has  not  been 
demonstrated,  though  according  to  the  experiment  of  Mr. 
Canton,  it  has  been  ascertained  that  there  are  slight  varia- 
tions during  the  different  months  of  the  year,  which  seem  to 
depend  on  the  degrees  of  heat  and  cold. 

962.  The  directive  power  of  the  magnet  is  of  vast  im- 
portance to  the  world,  since  by  this  power,  mariners  are 
enabled  to  conduct  their  vessels  through  the  widest  oceans, 
in  any  given  direction,  and  by  it  travellers  can  find  their 
way  across  deserts  which  would  otherwise  be  impassable. 


GALVANISM. 

963.  The  design  of  this  epitome  of  the  principles  of  Gal- 
vanism, is  to  prepare  the  pupil  to  understand  the  subject  of 
Electro-Magnetism,  which,  on  account  of  several  recent  pro- 
positions to  apply  this  power  to  the  movement  of  machinery, 
has  become  one  of  the  exciting  scientific  subjects  of  the  day. 

We  shall  therefore  leave  the  student  to  learn  the  history 
and  progress  of  Galvanism  from  other  treatises,  and  come  at 
once  to  the  principles  of  the  science. 

964.  When  two  metals,  one  of  which  is  more  easily  ox 
idated  than  the  other,  are  placed  in  acidulated  water,  and  the 
two  metals  are   made  to  touch  each  other,  or  a  metallic 
communication  is  made  between  them,  there  is  excited  an 
electrical  or  galvanic  current,  which  passes  from  the  metal 
most  easily  oxidated,  through  the  water,  to  the  other  metal, 

What  conditions  are  necessary  to  excite  the  galvanic  action  1  From 
which  metal  does  the  galvanism  proceed  1 


322 


GALVANISM. 


and  from  the  other  metal  through  the  water  around  10  die 
first  metal  again,  and  so  in  a  perpetual  circuit 

965.  If  we  take,  for  example,  a  slip  of  zinc,  and  another 
of  copper,  and  place  them  in  a  cup  of  diluted  sulphuric  acid, 
fig.  235,  their  upper  ends  in  contact,  and  above  the  water, 
and  their  lower  ends  separated,  then  Fig.  235. 
there  will  be  constituted  a  galvanic 

circle,  of  the  simplest  form,  consisting 
of  three  elements,  zinc,  acid,  copper. 
The  galvanic  influence  being  excited 
by  the  acid,  will  pass  from  the  zinc,  Z, 
the  metal  most  easily  oxidated,  through 
the  acid,  to  the  copper,  C,  and  from  the 
copper  to  the  zinc  again,  and  so  on 
continually,  until  one  or  the  other  of  the 
elements  is  destroyed,  or  ceases  to  act. 

966.  The  same  effect  will  be  produced,  if,  instead  of  allow- 
ing the  metallic  plates  to  come  in  contact,  a  communication 
between  them  be  made  by  means  of  wires,  as  shown  by  fig. 
236.      In  this  case,  as  well  _  Fig.  236. 

as  in  the  former,  the  electri- 
city proceeds  from  the  zinc, 
Z,  which  is  the  positive  side, 
to  the  copper,  C,  being  con- 
ducted by  the  wires  in  the  i 
direction  shown  by  the  ar-  1 
rows.  1 

967.  The  completion  of 
the  circuit  by  means  of  wires, 
enables  us  to  make  experi- 
ments on  different  substances 
by  passing  the  galvanic  in- 
fluence through  them,  this  being  the  method  employed  to 
exhibit  the  effects  of  galvanic  batteries,  and  by  which  the 
most  intense  heat  may  be  produced. 

COMPOUND  GALVANIC  CIRCLES. 

968.  In  the  above  instances  we  have  only  illustrations  of 
what  is  termed  a  simple  galvanic  circle,  the  different  ele- 
ments being  all  required  to  elicit  the  electrical  influence. 
When  these  elements  are  repeated,  and  a  series  is  formed, 

Describe  the  circuit.  What  is  the  effect  if  wires  be  employed  in- 
stead of  allowing  the  two  metals  to  touch  1  What  is  a  compound  gal- 
vanic circle  1 


GALVANISM.  32? 

ronsisting  of  zinc,  copper,  acid;  zinc,  copper,  acid,  there  is 
constituted  what  is  termed  a  compound  galvanic  circle.  It 
is  by  this  method  that  large  quantities  of  electricity  are  ob- 
tained, and  which  then  becomes  a  highly  important  chemical 
agent,  and  by  which  experiments  of  great  brilliancy  and  in- 
terest are  performed. 

969.  The  pile  of  Volta  was  one  of  the  earliest  means  by 
which  a  compound  galvanic  series  was  exhibited.     This 
consisted  of  a  great  number  of  silver  or  copper  coins,  and 
thin  pieces  of  zinc  of  the  same  dimensions,  together  with 
circular  pieces  of  card,  wet  with  an  acid,  piled,  one  series 
above  the  other,  in  the  manner  shown  by  fig.  237. 

970.  The  student  should  be  informed  that  it  makes  no 
difference  what  the  metals  are  which  form  the  galvanic 
series,  provided  one  be  more  easily  oxidated,  or  dissolved  in 
an  acid,  than  the  other,  and  that  the  Fig.  237. 

most  oxidable  one  always  forms 
the  positive  side.  Thus,  copper  is 
negative  when  placed  with  zinc,  but 
becomes  positive  with  silver. 

971.  The   three   substances   com- A 
posing  the  pile,  zinc,  silver,  wet  card,! 
and  marked  Z,  S,  W,  succeed  each  Pi 
other  in  the  same  order  throughout 
the  series,  and  its  power  is  equal  to 

a  single  circle,  multiplied  by  the  num- 
ber of  times  the  series  is  repeated. 

TROUGH  BATTERY. 

972.  The  galvanic  pile  is  readily  constructed,  and  an- 
swers for  small  experiments,  but  when  large  quantities  of 
electricity  are  required,   other  means  are  resorted  to,  and 
among  these,  what  is  termed  the  trough  battery  is  the  most 
convenient  and  efficacious. 

973.  The  zinc  and  copper  plates  are  fastened  to  a  slip  of 
mahogany  wood,  and  are  united  in  pairs  by  a  piece  of  metal 
soldered  to  each.     Each  pair  is  so  placed  as  to  enclose  a 
partition  of  the  trough  between  them,  each  cell  containing  a 
plate  of  zinc  connected  with  the  copper  plate  of  the  succeed- 
ing cell,  and  a  plate  of  copper  joined  with  the  zinc  plate  of 
the  preceding  cell. 

How  is  the  pile  of  Volta  constructed  7  What  qualities  are  requisite 
in  the  two  metals  in  order  to  yield  the  galvanic  influence  1  Describa 
the  trough  battery. 


324 


ELECTRO-MAGNETISM. 


974.  This  arrange-  Fig.  238. 
ment  will  be  under- 
stood by  figure  238, 

where  the  plates  P 
are  connected  in  the 
order  described,  and 
below  them  the  trough 
T,  to  contain  the  acid 
into  which  the  plates 
are  to  be  plunged. 

975.  The   trough 
re  made  of  wood,  with 
partitions  of  glass,  or 
what    is    better,    of 
Wedge  wood's   ware. 

Each  trough  contains  eight  or  ten  cells,  which  being  filled 
with  diluted  acid,  the  plates  are  suspended  and  let  down  into 
them  by  means  of  a  pulley.  The  advantage  of  this  method 
is,  that  the  plates  can  be  elevated  at  any  moment,  and  are 
easily  kept  clean  from  rust,  without  which  the  galvanic  ac- 
tion becomes  feeble. 

976.  A  great  variety  of  other  forms  of  metallic  combina- 
tions have  boen  devised  to  exhibit  the  galvanic  action,  but  the 
same  elements,  namely,  two  metals  and  an  acid,  are  required 
in  all,  nor  do  the  results  differ  from  those  above  described. 
The  several  kinds  of  galvanic  machines  already  described, 
are  therefore  considered  sufficient  for   the  objects  of  this 
epitome. 


ELECTRO-MAGNETISM. 

977.  Long  before  the  discovery  of  galvanism,  it  was  sus- 
pected by  those  who  had  made  the  subjects  of  magnetism  and 
electricity  objects  of  experiment  and  research,  that  there  ex- 
isted an  affinity  or  connection  between  them.  In  the  year 
1774,  one  oflhe  philosophical  societies  of  Germany  pro- 
posed as  the  subject  of  a  prize  dissertation,  the  question,  "  Is 
there  a  real  and  physical  analogy  between  the  electric  and 
magnetic  forces?"  The  question  was,  however,  then  an- 
swered in  the  negative ;  but  naturalists  still  appear  to  have 
kept  the  same  subject  in  view,  and  by  the  observation  of 

What  are  the  advantages  of  the  trough  battery  1  What  is  said  of  the 
suspicion  of  analogy  between  electricity  and  magnetism  before  the  dis- 
covery of  galvanism  1 


ELECTRO-MAGNETISM.  325 

new  facts,  the  existence  of  such  an  analogy  was  from  time 
to  time  affirmed  by  various  philosophers. 

978.  The  aurora  borealis,  which  has  long  been  supposed 
to  be  an  electrical  phenomenon,  was  observed  to  influence 
the   magnetic   needle ;   and  lightning,  well   known  to  be 
nothing  more  than  an  electrical  movement,  was  known  in 
many  instances  to  have  destroyed  or  reversed  the  polarity  of 
trie  compass. 

979.  An  instance  of  this  kind,  which  might  have  led  to 
very  disastrous  consequences,  is  related  of  a  ship  in  the 
midst  of  the  Atlantic,  which  being  struck  with  lightning, 
had  the  polarity  of  all  her  compasses  reversed.     This  being 
unknown,  the  ship  was  directed  as  usual  by  the  compass, 
until  the  ensuing  evening,  when  the  stars  showed  that  her 
direction  was  in  the  exact  opposite  course  from  what  was 
intended,  and  then  it  was  that  the  phenomenon  in  question 
was  first  suspected. 

980.  These  discoveries  of  course  led  philosophers  to  try 
the  effects  of  powerful  electrical  batteries  on  pieces  of  steel, 
and  although  polarity  was  often  induced  in  this  manner,  yet 
the  results  were  far  from  being  uniform,  and   the  experi- 
ments  on  this   subject  seem  in  a  measure  to  have  ceased, 
when  the  discovery  of  the  galvanic  influence  opened  a  new 
field  of  inquiry,  and  gave  such  an  impulse  to  the  labours, 
investigations,  and  experiments  of  philosophers  throughout 
Europe,  as  perhaps  no  other  subject  had  ever  done. 

981.  It  was,  however,  more  than  twenty  years  from  the 
time  of  Galvani's  discovery,  before  the  science  of  Electro- 
Mao-netism  was  developed,  the  first  having  taken  place  in 
1791,  while  the  experiments  of  M.  Oersted,  the  real  disco- 
verer of  Electro-Magnetism,  were  made  in  1819. 

982.  M.  Oersted  was  Professor  of  Natural  Philosophy, 
and  Secretary  to  the  Royal  Society  of  Copenhagen.      His 
experiments,  and  others  on  the  subject  in  question,  are  de- 
tailed at  considerable  length,  and  illustrated  by  many  draw- 
ings, but  we  shall  here -only  give  such  an  abstract  as  to  make 
the  subject  clearly  understood. 

983.  The  two  poles  of  the  battery,  fig.  255,  are  connected 
by  means  of  a  copper  wire  of  a  yard  or  two  in  length,  the 
two  parts  being  supported  on  a  table  in  a  north  and  south 
direction,  for  some  of  the  experiments,  but  in  others  the  di- 

Is  there  any  connection  between  the  aurora  borealis  and  the  magnetic 
needle  1  What  is  said  to  have  been  the  effect  of  lightning  on  the 
-ompasses  of  a  ship  at  sea?  What  is  the  uniting  wire  1 


326  ELECTRO-MAGNETISM. 

rection  must  be  changed,  as  will  be  seen.     This  wire,  it  will 
be  remembered,  is  called  the  uniting  wire. 

984.  Being  thus  prepared,  and  the  galvanic  battery  in 
action,  take  a  magnetic  needle  six  or  eight  inches  long,  pro- 
perly balanced  on  its  pivot,  and  having  detached  the  wire 
from  one  of  the  poles,  place  the  magnetic  needle  under  the 
wire,  but  parallel  with  it,  and  having  waited  a  moment  foi 
the  vibrations  to  cease,  attach  the  uniting  wire  to  the  pole. 
The  instant  this  is  done,  and  the  galvanic  circuit  completed, 
the  needle  will  deviate  from  its  north  and  south  position, 
turning  towards  the  east  or  west,  according  to  the  direction 
in  which  the  galvanic  current  flows.     If  the  current  flows 
from  the  north,  or  the  end  of  the  wire  along  which  it  passes 
to  the  south  is  connected  with  the  positive  side  of  the  battery, 
then  the  north  pole  of  the  needle  will  turn  towards  the  east; 
but  if  the  direction  of  the  current  is  changed,  the  same  pole 
will  turn  in  the  opposite  direction. 

985.  If  the  uniting  wire  is  placed  under  the  needle,  in- 
stead of  over  it,  as  in  the  above  experiment,  the  contrary  ef 
feet  will  be  produced,  and  the  north  pole  will  deviate  to- 
wards the  west. 

986.  These  deviations  will  be  understood  by  the  follow- 
ing figures.     In  fig.  239,  N  presents  the  north,  and  S  the 
south  pole  of  the  magnetic  nee-  Fig.  239. 

die,  and  p  the  positive  and  n  the  P  — >  iv_ 

negative   ends   of   the    uniting  ^         E 

wire.      The    galvanic  current,       ..•-"v::  •.'•;•  ••-.. 

therefore,  flows  from  p  towards  u 
n,  or,  the  wire  being  parallel 
with  the  needle,  from  the  north 
towards  the  south,  as  shown  by 
the  direction  of  the  arrow  in  the 
figure. 

Now  the  uniting  wire  being  above  the  needle,  the  pole 
N,  which  is  towards  the  positive  side  of  the  battery,  will  de- 
viate towards  the  east,  and  the  needle  will  assume  the  diree 
tion  N'  S'. 

On  the  contrary,  when  the  uniting  wire  is  carried  below  tht. 
needle,  the  galvanic  current  being  in  the  same  direction  ;i? 
before,  as  shown  by  fig.  240,  then  the  same,  or  north  pole, 
will  deviate  towards  the  west,  or  in  the  contrary  direction  from 
the  former,  and  the  needle  will  assume  the  position  N'  S'. 

If  the  needle  is  stationary,  and  the  current  flows  from  the  north,  what 
way  will  the  needle  ktrn  1  Explain  fig.  239. 


ELECTRO-MAGNETISM. 


J!^S 


987.  When  the  uniting  wire  Fig.  240. 
is  situated  in  the  same  horizon-  ^ 
tal  plane  with  the  needle,  and  is 

parallel  'to  it,  no  movement  , 
takes  place  towards  the  east  or 
west ;  but  the  needle  dips,  or  the 
end  towards  the  positive  end  of 
the  wire  is  depressed,  when  the 
wire  is  on  the  east  side,  and  ele- 
vated when  it  is  on  the  west  side. 

Thus,  if  the  uniting  wire  p  n,  Fig.  241. 

fig.  241,  is  placed  on  the,  east       :cr*  f  s' 

side  of  the  needle  N  S,  and  paral-  ^        \  ..^        n 

lei  to,  and   on  a  level  with  it,     '       •*   '  -..      s,:>7  = 

then  the  north  pole,  N,  being  H. 
towards  the  positive  end  of  the 
wire,  will  be  elevated,  and  the 
needle  will  assume  the  position 
of  the  dotted  needle  N'  S'.  But 
if  the  wire  be  changed  to  the 
western  side,  other  circumstances  being  the  same,  then  the 
north  pole  will  be  depressed,  and  the  needle  will  take  the 
direction  of  the  dotted  line  N"  S". 

988.  If  the  uniting  wire,  instead  of  being  parallel  to  the 
needle,  be  placed  at  right  angles  with  it,  that  is,  in  the  direc- 
tion of  east  and  west,  and  the  needle  brought  near,  whether 
above  or  below  the  wire,  then  the  pole  is  depressed  when 
the  positive  current  is  from  the  west,  and  elevated  when  it  is 
from  the  east. 

Thus,  the  pole  S,  fig.  242,  is  elevated,  the  current  of 
positive  electricity  being  from 
p  to  n,  that  is,  across  the  nee- 
dle from  the  east  towards  the 
west.  If  the  direction  of  the 
positive  current  is  changed, 
and  made  to  flow  from  n  to 
p  the  other  circumstances 
being  .the  same,  the  south 
pole  of  the  needle  will  be  de- 
pressed. 

989.  When  the  uniting  wire,  instead  of  being  placed  in  a 
horizontal  position  as  in  the  last  experiment,  is  placed   ver- 

Explain  figures  240,  241,  and  242. 


*^^  ^S 


d*> 


328  ELECTRO-MAGNETISM. 

tically,  either  to  the  north  Fig.  243. 

or  south  of  the  needle,  and 
near  its  pole,  as  shown  by 
fig.  243,  then  if  the  lower 
extremity  of  the  wire  re- 
ceives the  positive  current, 
as  from  p  to  n,  the  needle 
will  turn  its  pole  towards 
the  west. 

If  now  the  wire  be  made 
to  cross  the  needle  at  a  point  about  half  way  between  the 
pole  and  the  middle,  the  same  pole  will  deviate  towards  the 
east.     If  the  positive  current  be  made  to  flow  from  the  upper 
end  of  the  wire,  all  these  phenomena  will  be  reversed. 
LAWS  OF  ELECTRO-MAGNETIC  ACTION. 

990.  An  examination  of  the  facts  which  may  be  drawn 
from  an  attentive  consideration  of  the  above  experiments,  are 
sufficient  to  show  that  the  magnetic  force  which  emanates 
from  the  conducting  wire,  is  different  in  its  operation  from 
any  other  force  in  nature,  with  which  philosophers  had  been 
acquainted. 

991.  This  force  does  not  act  in  a  direction  parallel  to  that 
of  the  current  which  passes  along  the  wire,  "  but  its  action 
produces  motion  in  a  circular  direction  around  the  wire,  that 
is,  in  a  direction  at  right  angles  to  the  radius,  or  in  the  di- 
rection of  the  tangent  to  a  circle  described  round  the  wire- 
in  a  plane  perpendicular  to  it." 

992.  In  consequence  of  this  circular  current,  which  seems 
to  emanate  from  the  regular  polar  currents  of  the  battery, 
the  magnetic  needle  is  made  to  assume  the  positions  indi- 
cated by  the  figures  above  described,  and  the  effect  of  which 
is,  to  change  the  direction  of  the  needle  from  the  magnetic 
meridian,  moving  it  through  the  section  of  a  circle  in  a  di- 
rection depending  on  the  relative  position  of  the  wire  and 
the  course  of  the  electric  fluid.     And  we  shall  see  hereafter 
that  there  is  a  variety  of  methods  by  which  this  force  can  be 
applied  to  produce  a  continued  circular  motion. 
CIRCULAR  MOTION  OF  THE  ELECTRO-MAGNETIC  FLUID. 

993.  We  have  already  stated  that  the  action  of  this  fluid 
produces  motion  in  a  circular  direction.     Thus,  if  we  sup- 
Explain  figure  243.     Does  the  magnetic  force  of  galvanism  differ 

from  any  force  before  known,  or  not  1     In  what  direction  does  this 
force  act,  as  it  passes  along  the  wire  1 


ELECTRO-MAGNETISM. 


329 


pose  the  conducting  wire  to  be  placed  in  a  vertical  situation, 
as  shown  by  fig.  244, 
and  p  ra,  the  current  of 
positive  electricity,  to 
be  descending  through 
it,  from  p  to  n,  and  if 
through  the  point  c  in 
the  wire  the  plane  N 
N  be  taken,  perpendi- 
cular to  p  n,  that  is  in 
the  present  case  a  hori- 
zontal plane,  then  if 
any  number  of  circles 
be  described  in  that 
plane,  having  c  for  their 
common  centre,  the  ac- 
tion of  the  current  in  the  wire  upon  the  north  pole  of  the 
magnet,  will  be  to  move  it  in  a  direction  corresponding  to 
the  motion  of  the  hands  of  a  watch,  having  the  dial  towards 
the  positive  pole  of  the  battery.  The  arrows  show  the  di- 
rection of  the  current's  motion  in  the  figure. 

994.  When  the  direction  of  the  electrical  current  is  re- 
versed, the  wire  still  having  its  vertical  position,  the  direc- 
tion of  the  circular  action  is  also  reversed,  and  the  motion  is 
that  of  the  hands  of  the  watch  moving  backwards. 

As  the  magnetic  needle  cannot  perform  entire  revolutions 
when  it  is  crossed  by  the  conducting  wire,  it  becomes  neces- 
sary, in  order  to  show  clearly  that  such  a  circulation  as  we 
have  supposed  actually  exists,  to  describe  more  clearly  than 
we  have  yet  done,  the  means  of  demonstrating  such  an  ac- 
tion, and  the  corresponding  motion. 

995.  Now  the  metals  being  conductors  of  the  electric  fluid, 
if  we  employ  one  through  the  substance  of  which  the  mag- 
netic needle  can  move,  we  shall  have  an  opportunity  of  know- 
ing whether  the  fluid  has  the  circular  action  in  question, 
for  then  the  needle  will  have  liberty  to  move  in  the  direction 
of  the  electrical  current. 

996.  For  this  purpose  mercury  is  well  adapted,  being  a 
good  conductor  of  electricity,  and  at  the  same  time«o  fluid 
as  to  allow  a  solid  to  circulate  in  it,  or  on  its  surface,  with 


Explain  by  fig.  244  in  what  direction  the  electro-magnetic  fluid  moves. 
Why  is  mercury  v/eTi  adapted  to  show  the  circular  action  of  the  gal- 
vanic fluid  1 

28* 


330 


ELECTRO-MAGNETISM. 


considerable  facility.     This,  ^therefore,  is  the  substance  em- 
ployed in  these  experiments. 

MEANS  OF  PRODUCING  ELECTRO-MAGNETIC  ROTATIONS 

997.  The  continued  revolution  of  one  of  the  poles  of  a 
mag-net  round  a  vertical  conducting  Wire,  may  be  produced 
in  the  following  manner : — 

The  small  glass  cup,  fig.  245,  of  which  the  right  hand 
cut  is  a  section,  is  pierced  Fig.  245.  c 

at  the  bottom  for  the  ad- 
mission of  the  crooked 
piece  of  copper  wire  d, 
which  is  made  to  commu- 
nicate with  one  of  the  poles 
of  a  galvanic  battery.  To 
the  end  of  this  wire,  which 
projects  within  the  cup,  is 
attached  by  means  of  a 
fine  thread,  the  end  of  the 
magnet  a.  The  string 
must  be  of  such  length  as ' 
to  allow  the  upper  end  of  the  magnet  to  reach  nearly  the  top 
of  the  cup.  The  vertical  wire  c  is  the  positive  pole  of  the 
battery. 

998.  Having  made  these  preparations,  fill  the  cup  so  full 
of  mercury  as  only  to  allow  a  small  portion  of  the  upper  end 
of  the  magnet  to  float  above  the  surface,  as  shown  in  the 
figure.     Then,  by  means  of  a  little  frame,  or  otherwise,  fix 
the  copper  wire  of  the  positive  pole  in  the  centre  of  the 
mercury,  letting  it  dip  a  little  below  the  surface,  and  on  con- 
necting the  negative  pole  with  the  wire  d,  the  magnet  will 
revolve  round  the  copper  wire,  and  continue  to  do  so  as  long 
as  the  connection  between  the  two  poles  of  the  battery  and 
the  mercury  remains  unbroken. 

999.  To  insure  close  contact  between  the  poles  of  the  bat- 
tery and  the  mercury,  the  ends  of  the  wires  where  they  dip 
into  the  mercury  are  amalgamated,  which  is  done  by  means 
of  a  little  nitrate  of  mercury,  or  by  rubbing  them,  being  of 
copper,  with  the  metal  itself. 


Explain  fig.  245,  and  show  how  the  pole  of  a  magnet  may  be  made  to 
move  in  a  circle.  In  these  experiments,  why  are  the  ends  of  the  con- 
ducting wires  amalgamated  1 


ELECTRO-MAGNETISM.  331 

REVOLUTION  OF  THE  CONDUCTING  WIRE   ROUND  THE 
POLE  OF  THE  MAGNET. 

1000.  In  the  above  example  the  wire  is  fixed,  while  the 
electrical  current  gives  motion  to  the  magnet.     But  this  or- 
der may  be  reversed,  and  the  wire  made  to  revolve,  while 
the  magnet  is  stationary. 

1001.  The  apparatus  for  this  purpose  is  represented  by 
fig.  246,  and  consists  of  a  shallow  glass  cup,  with  a  tubu- 
lar  stem  to   hold   the  Fig.  246. 

mercury.  In  the  stem, 
as  seen  in  the  section  on 
the  right,  there  is  a 
small  copper  socket, 
which  is  fixed  there  by 
being  fastened  to  a  cop- 
per plate  below,  which 
plate  is  cemented  to  the 
glass  so  that  no  mer- 
cury can  escape.  This 
plate  is  tinned  and 
amalgamated  on  the 
under  side,  and  stands 
on  another  plate,  the 
upper  side  of  which  is 
also  tinned  and  amal- 
gamated, and  between 
these  the  conducting  wire  passes,  so  as  to  insure  a  perfect 
metallic  continuity  between  the  poles  of  the  battery. 

A  strong  cylindrical  magnet  is  placed  in  the  copper 
socket,  with  its  upper  end  so  high  as  to  reach  a  little  above 
the  mercury  when  the  cup  is  filled.  The  wire  connected 
with  the  pole  of  the  battery,  which  dips  into  the  mercury,  is 
suspended  by  means  of  loops,  as  seen  in  the  figures. 

1002.  When  the  apparatus  is  thus  arranged,  and  a  com- 
munication made  through  it,  between  the  poles  of  the  bai- 
tery,  the  wire  will  revolve  round  the  magnet  with  great  ra- 
pidity. 

1003.  A  more  simple  apparatus,  answering  a  similar  pur- 
pose, and  in  which  the  wire  revolves  very  rapidly,  with  a 
very  small  voltaic  power,  is  represented  by  fig.  247. 

1004.  It  consists  of  a  piece  of  glass  tube,  g  g,  the  lower  end 
of  which  is  closed  by  a  cork,  through  which  a  small  piece 
of  soft  iron  wire,  m,  is  passed,  so  as  to  project  above  and  below. 

Explain  fig.  246. 


332 


ELECTRQ-31  A.GNET  ISM . 


A  little  mercury  is  then  poured  in  so  as  to  Fig.  247. 
make  a  channel  between  the  wire  and  the  glass 
tube.  The  upper  orifice  of  the  tube  is  also 
closed  by  a  cork,  through  which  a  piece  of 
copper  wire,  b,  passes,andterminates  in  a  loop. 
Another  piece  of  wire,  c,  is  suspended  from 
this  by  a  loop,  the  end  of  which  dips  into  the 
mercurv,  and  is  amalgamated. 

1005.  In   this    arrangement,    a    temporary 
magnet  is  formed  of  the  soft  iron  wire,  m  a,  by 
the  electrical   fluid,    and   around    which    the  o\ 
moveable  wire,  c,  revolves  rapidly,  changing 
its   direction,  as  usual,  when  the  direction  of 
the  current  is  changed. 

REVOLUTION    OF    A    MAGNET    ROUND    ITS 
OWN  AXIS. 

1006.  After  it  was  found  that  a  conducting 
wire  might  be  made  to  revolve  round  a  mag- 
net, and  a  magnet  round  a  conducting  wire, 
many  attempts  were  made  to  obtain  the   rota- 
tion of  a  magnet  and  of  a  conductor  around 
their  own  axes. 

The  rotation  of  a  magnet  on  its  axis  may  be  accomplished 
by  means  of  galvanism,  by  the  following  method  : — 

1007.  The  cylindrical  magnet,  a, 
fig.  248,  terminates  at  its  lower  ex- 
tremity in  a  sharp  point,  which  rests 
in  a  conical  cavity  of  agate,  so  as 
much  as  possible  to  avoid  friction. 
The  vessel,  the  section  of  which  is 
here   shown,    may  be    of  glass   or 
wood.     The  upper  end  of  The  mag- 
net is  supported  in  the  perpendicular 
position  by  a  thin  slip  of  wood,  pass- 
ing across  the  upper  part  of  the  ves- 
sel, and  having  an  aperture  through 
it,  of  proper  size. 

1008.  A  piece  of  quill  is  fitted  on 
the  upper  end  of  the   magnet,  and 
rising  a  little  above  it,  forms  a  cup 
to  hold  a  globule  of  mercury.      Into 
this  mercury  is  inserted  the  lower 
end  of  the  wire  c,  which  has  a  cup  on 

Explain  figures  247  and  x?48. 


ELECTRO-MAGNETISM. 


333 


the  top,  containing  mercury  for  the  usual  purpose.  The  end 
of  the  wire  c  must  be  amalgamated,  as  also  the  termination 
of  the  poles  of  the  battery,  which  dip  into  the  cups  c  and  d. 
A  copper  wire  of  considerable  size  pierces  the  bottom  of  the 
vessel,  and  ends  in  the  cup  d,  like  the  other,  containing  mer- 
cury, in  order  to  make  the  contact  perfect. 

The  vessel  being  now  filled  with  mercury  nearly  up  to  a, 
so  as  to  cover  about  one  half  the  magnet,  and  the  ends  of  the 
galvanic  poles  inserted  into  the  cups  c  and  d,  the  magnet  be- 
gins to  revolve,  and  continues  to  do  so  as  long  as  the  con- 
nection is  unbroken. 

1009.  In  order  to  produce  the  rotation  of  a  magnet,  it  is 
necessary  that  the  electrical   influence,  in  every  instance, 
should  act  only  on  one  of  the  poles  at  the  same  time,  because 
the  direction  of  the  current  on  the  two  ends  are  contrary  to 
each  other,  and  therefore  the  two  forces  would  be  neutral- 
ized, and  no  motion  be  produced. 

In  the  above  experiment,  the  electrical  current,  having 
passed  the  upper  half  of  the  magnet,  is  diffused  in  the  mer- 
cury in  which  the  lower  half  is  Fig.  249. 
buried,  and  thus  produces  no 
sensible  effect  upon  it. 

1010.  Another  method  of  pro- 
ducing   the   rotation  of   a   mag- 
net, is   represented  by  fig.   249. 
In  this,  a  is  a  cylindrical  mag- 
net pointed  at  both  ends,  and  run- 
ning in   an  agate  cup,  which   is 
fixed  on  a  stem  rising  from  the 
bottom  of  the  stand.      Its    upper 
point  runs  in  a  little  cavity  in  the 
end  of  the  thumb  screw  b,  which 
passes   through   the   cap   of  the 
frame-work  of  the  apparatus.  Near 
the  middle  of  the  magnet,   this 
frame,  which  is  of  wood,  supports 
a  shelf,  on  which  rests  the  circu- 
lar cistern  of  mercury,  c,  the  mag-1 
net  passing   freely   through   the 
centre   of   both.      A   cistern    of 
mercury,    d,  also  surrounds  the 

To  produce  the  rotation  of  a  magnet,  on  what  part  must  the  galvan* 
ism  act  1  Why  1  Explain  fig.  249,  and  show  the  course  of  the  elec- 
trical fluid  from  one  CUD  to  the  other. 


334  ELECTRO-MAGNETISM. 

Aower  point  of  the  magnet,  and  in  the  centre  of  which  is 
placed  the  agate  cup.  A  piece  of  copper  wire  projecting 
into  the  interior  of  these  cisterns,  terminates  in  a  cup  holding 
mercury,  for  the  purpose  of  effecting  a  communica- 
tion with  the  galvanic  battery,  in  the  usual  manner.  A 
small  wire  of  copper,  pointed,  and  amalgamated  at  the  lower 
end,  is  fastened  to  the  magnet,  and  made  to  dip  into  each  of 
the  cisterns  of  mercury,  as  seen  in  the  figure. 

1011.  In  this  arrangement,  the  lower  half  of  the  magnet 
only,  forms  a  part  of  the  galvanic  circle,  the  fluid  passing 
in  at  one  cup  and-out  at  the  other  hy  the  following  routine, 
which  is  apparent  by  the  figure.  Suppose  the  positive  wire  is 
placed  in  the  upper  cup,  then  the  circuit  will  be  from  the 
cup  along  the  wire  to  the  mercury  in  the  cistern,  and  from 
the  mercury  through  the  bent  wire  to  the  magnet — down  the 
magnet  through  the  lower  bent  wire  to  the  mercury,  and 
thence  to  the  cup,  and  the  negative  pole  of  the  battery. 

When  the  galvanic  current  is  thus  established,  the  rota- 
tion of  the  magnet  begins,  and  if  the  points  of  the  axis  are 
delicate,  and  the  friction  small,  it  will  revolve  rapidly. 

VIBRATORY    AND    ROTATORY    MOTIONS    PRODUCED    BY 
MEANS  OF  HORSE-SHOE  MAGNETS. 

1012.  By  the  use  of  these  magnets,  both  the  magnetic 
poles  conspire  to  give  the  motion.     The  influence  of  the  two 
poles  being  in  contrary  directions,  and  so  near  each  other 
that  the  wire  or  wheel  placed  between  them  are  within  the 
magnetic  currents  of  both,  the  effect  appears  to  be,  to  form  a 
current  at  right  angles  to  the  vibrating  wire.     The  wire  be- 
comes magnetic  by  the  galvanic  power,  every  time  it  touches 
the  mercury  between  the  poles  of  the  magnet,  and  conse- 
quently is  thrown  backwards  or  forwards  by  the  magnetic 
current,  according  to  its  direction;  hence,  if  the  poles  of  the 
battery  are  charged  so  as  to  carry  the  electricity  in  a  con- 
trary direction  through  the  apparatus,  the  impulse  on  the 
wire  or  wheel  will  also  be  changed  to  the  opposite  direc- 
tion.    If  the  poles  of  the  magnet  be  changed,  by  turning  it 
over,  the  same  effect  will  be  produced,  and  the  wheel  will 
revolve  in  a  contrary  direction  from  what  it  did  before. 

1013.  Thus,  if  the  magnet  be  laid  in  the  direction  of 
north  and  south,  with  the  poles  towards  the  north,  the  north 
pole  be^ng  on  the  east  side,  and  the  positive  electricity  be 

How  may  the  direction  of  the  vibrating  wire  be  changed  ? 


ELECTRO-MAGNETISM.  335 

sent  through  the  vibrating  wire,  upwards,  then  the  vibrating 
force  will  be  towards  the  north  ;  but  if  either  the  poles  of  the 
magnet  or  those  of  the  battery  be  changed,  the  wire  will  be 
thrown  towards  the  south. 

VIBRATION  OF  A  WIRE. 

1014.  A  conducting  copper  wire,  w>  fig.  250,  is  suspend- 
ed by  a  loop  from  a  hook  of  the  same  metal,  wThich  passes 


Fig.  250. 


through  an  arm  of  metal  or 
wood,  as  seen  in  the  cut.  The 
upper  end  of  the  hook  terminates 
in  the  cup  P,  to  contain  mer- 
cury. The  lower  end  of  the 
copper  wire  just  touches  the 
mercury,  Q,,  contained  in  a  lit- 
tle trough  about  an  inch  long1, 
formed  in  the  wood  on  which 
the  horse-shoe  magnet,  M,  is 
laid,  the  mercury  being  equally 
distant  from  the  two  poles. 

The  cup,  N,  has  a  stem  of 
wire.,  Avhich  passes  through  the 
wood  of  the  platform  into  the 
mercury,  this  end  of  the  wire 
being  tinned,  or  amalgamated, 
so  as  to  form  a  perfect  contact. 

1015.  Having  thus  prepared 
the  apparatus,  put  a  little  mercury  into  the  cups  P  and  N, 
and  then  form  the  galvanic  circuit  by  placing  the  poles  of 
the  battery  in  the  two  cups,  and  if  every  thing*  is  as  it 
should  be,  the  wire  will  begin  to  vibrate,  being  thrown  with 
considerable  force  either  towards  M  or  Q,,  according  to  the 
position  of  the  magnetic  poles,  or  the  direction  of  the  cur- 
rent, as  already  explained.  In  either  case  it  is  thrown  out 
of  the  mercury,  and  the  galvanic  circuit  being  thus  broken, 
the  effect  ceases  until  the  wire  falls  back  again  by  its  own 
weight,  and  touches  the  mercury,  when  the  current  being 
again  perfected,  the  same  influence  is  repeated,  and  the  wire 
is  again  thrown  away  from  the  mercury,  and  thus  the  vibra- 
tory motion  becomes  constant. 

This  forms  an  easy  and  beautiful  electro-magnetic  experi- 
ment, and  may  be  made  by  any  one  of  common  ingenuity, 

Explain  fig.  250,  and  describe  the  course  of  the  electric  fluid  from 
one  cup  to  the  other 


336 


ELECTRO-MAGNETISM. 


who  possesses  a  galvanic  battery,  even  of  small  power,  and 
a  good  horse-shoe  magnet. 

1016.  The  platform  may  be  nothing  more  than  a  piece  of 
pine  board  eight  inches  long  and  six  wide,  with  two  sticks 
of  the  same  wood,  forming  a  standard  and  arm  for  suspend- 
ing the  vibrating  wire.     The  cups  may  be  made  of  percus- 
sion caps,  exploded,  and  soldered  to  the  ends  of  pieces  of  cop- 
per bell  wire. 

1017.  The  wire  must  be  nicely  adjusted  with  respect  to 
the  mercury,  for  if  it  strikes  too  deep,  or  is  too  far  from  the 
surface,  no  vibrations  will  take  place.     It  ought  to  come  so 
near  the  mercury  as  to  produce  a  spark  of  electrical  fire,  as 
it  passes  the  surface,  at  every  vibration,  in  which  case  it  may 
be  known  that  the  whole  apparatus  is  well  arranged.     The 
vibrating  wire  must  be  pointed  and  amalgamated,  and  may 
be  of  any  length,  from  a  few  inches  to  a  foot  or  two. 

ROTATION  OF  A  WHEEL. 

1018.  The  same  force  which  throws  the  wire  away  from 
the  mercury,  will  cause  the  rotation  of  a  spur-wheel.     For 
this  purpose  the  conducting  wire,  Fig.  251. 
instead  of  being  suspended  as  in 

the  former  experiment,  must  be 
fixed  firmly  to  the  arm,  as  shown 
by  fig.  251.  A  support  for  the 
axis  of  the  wheel  may  be  made 
by  soldering  a  short  piece  to  the 
side  of  the  conducting  wire,  so 
as  to  make  the  form  of  a  fork, 
the  lo\ve£  ends  of  which  must  be 
flattened  with  a  hammer,  and 
pierced  with  fine  orifices,  to  re- 
ceive the  ends  of  the  axis. 

1019.  The   apparatus    for  a 
revolving  wheel  is  in  every  re- 
spect like  that  already  described 
for  the  vibrating  wire,  except  in 
that  above  noticed.     The  wheel 
may  be  made  of  brass  or  copper, 

but  must  be  thin  and   light,  and  so  suspended  as  to  move 
freely  and  easily.     The  points  of  the  notches  must  be  amal- 

How  must  the  points  of  the  vibrating  wire  be  adjusted  in  order  to 
act"?  Explain  fig. 251.  In  what  manner  may  the  points  of  the  spur 
wheel  be  amalgamated  1 


ELECTRO-MAGNETISM.  337 

gamated,  which  is  done  m  a  few  minutes,  by  placing  the 
wheel  on  a  flat  surface,  and  rubbing  them  with  mercury  by 
means  of  a  cork.  A  little  diluted  acid  from  the  galvanic 
battery  will  facilitate  the  process.  The  wheel  may  be  from 
half  an  inch  to  several  inches  in  diameter.  A  cent  ham- 
mered thin,  which  may  be  done  by  heating  it  two  or  three 
times  during  the  process,  and  then  made  perfectly  round, 
and  its  diameter  cut  into  notches  with  a  file,  will  answer 
every  purpose. 

1 020.  This  affords  a  striking  and  novel  experiment ;  for 
when  every  thing  is  properly  adjusted,  the  wheel  instantly 
begins  to  revolve  by  touching  with  one  of  the  wires  of  the 
battery  the  mercury  in  the  cup  P  or  N. 

When  the  poles  of  the  magnet,  or  those  of  the  battery,  are 
changed,  the  wheel  instantly  revolves  in  a  contrary  direction 
from  what  it  did  before. 

1021.  It  is,  however,  not  absolutely  necessary  to  divide 
the  wheel  into  notches,  or  rays,  in  order  to  make  it  revolve, 
though  the  motion  is  more  rapid,  and  the  experiment  suc- 
ceeds much  better  by  doing  so. 

REVOLUTION  OF  TWO  WHEELS. 

1022.  If  two  wheels  be  arranged  as  represented  by  fig 
252,  they  will  both  re-  ^  i     Fig.  252. 

volve  by  the  same  elec- 
trical current.  Eachpj 
horse-shoe  magnet  has 
its  trough  of  mercury. 
The  magnets  have  been 
omitted  in  the  drawing,  but  are  to  be  placed  precisely  as  in 
the  last  figure.  The  electrical  communication  is  to  be  made 
through  the  cups  of  mercury,  P  and  N,  and  its  course  is  as 
follows: — From  the  cup  it  passes  into  the  mercury j  from 
the  mercury  through  the  radii  to  the  axis  of  the  wheel,  and 
along  the  axis  to  the  other  wheel,  down  which  it  passes  to 
the  mercury,  and  so  to  the  other  cups,  and  to  the  opposite 
pole  of  the  battery. 

The  poles  of  the  magnets  for  this  experiment,  must  be 
opposed  to  each  other. 

ELECTRO-MAGNETIC  INDUCTION. 

1023.  Experiment  proves  that  the  passage  of  the  gal- 
vanic current  through  a  copper  wire  renders  iron  magnetic 

Explain  fig.  252,  and  show  how  two  wheels  may  be  made  to  revolve 
by  the  same  current. 

23 


338  ELECTRO-MAGNETISM. 

when  in  the  vicinity  of  the  current.     This  is  called  mag 
netic  induction. 

1 024.  The  apparatus  for  this  purpose  is  represented  by 
fig.  253,  and  consists  of    _  Fig.  253. 

a  copper  wire  coiled,  by 
winding  it  around  a 
piece  of  wood.  The 
turns  of  the  wire  should 
be  close  together  for 
actual  experiment,  they 
being  parted  in  the  figure  to  show  the  place  of  the  iron  to 
be  magnetized.  The  best  method  is,  to  place  the  coiled 
wire,  which  is  called  an  electrical  helix,  in  a  glass  tube,  the 
two  ends  of  the  wire  of  course  projecting.  Then  placing 
the  body  to  be  magnetized  within  the  folds,  send  the  gal- 
vanic influence  through  the  whole,  by  placing  the  poles  of 
the  battery  in  the  cups. 

1025.  Steel   thus   becomes    permanently  magnetic,   the 
poles,  however,  changing  as  often  as  the  fluid  is  sent  through 
it  in  a  contrary  direction.     A  piece  of  watch-spring  placed  in 
the  helix,  and  then  suspended,  will  exhibit  polarity,  but  if 
its  position  be  reversed  in  the  helix,  and  the  current  again 
sent  through  it,  the  north  pole  will  become  south.     If  one 
blade  of  a  knife  be  put  into  one  end  of  the  helix,  it  will  re- 
pel the  north  pole  of  a  magnetic  needle,  and  attract  the 
south  ;  and  if  the  other  blade  be  placed  in  the  opposite  end 
of  the  helix,  it  will  attract  the  north  pole,  and  repel  the 
south,  of  the  needle. 

1026.  Temporary  Magnets. — Temporary  magnets,  of  al- 
most any  power,  may  be  made  by  winding  a  thick  piece 
of  soft  iron  with  many  coils  of  insulated  copper  wire. 

The  best  form  of  a  magnet  for  this  purpose  is  that  of  a 
horse-shoe,  and  which  may  be  made  in  a  few  minutes  by 
heating  and  bending  a  piece  of  cylinder  iron,  an  inch  or 
two  in  diameter,  into  this  form. 

1027.  The  copper  wire  (bell  wire)  may  be  insulated  by 
winding  it  with  cotton  thread.     If  this  cannot  be  procured, 
common  bonnet  wire  will  do,  though  *t  makes  less  powerful 
magnets  than  copper. 


What  is  meant  by  magnetic  induction  1  Explain  fig.  253.  What  is 
this  figure  called  1  Does  any  substance  become  permanently  magnetic 
by  the  action  of  the  electrical  helix  1  How  may  the  poles  of  a  magnet 
be  changed  by  the  helix  1  How  may  temporary  magnets  be  made  ? 


ELECTRO-MAGNETISM.  339 

1028.  The  coils  of  wire  may  begin  near  one  pole  of  the 
magnet  and  terminate  near  the  other,  as  represented  by  fig. 
254,  or   the  wire   may  Fig.  254. 

consist  of  shorter  pieces 
wound  over  each  other, 
on  any  part  of  the  mag- 
net. In  either  case,  the 
ends  of  the  wire,  where 
several  pieces  are  used, 
must  be  soldered  to  two 
strips  of  tinned  sheet 
copper,  for  the  com-p 
bined  positive  and  nega- 
tive poles  of  the  wires. 
To  form  the  magnet, 
these  pieces  of  copper 
are  made  to  communi- 
cate with  the  poles  of 
the  battery,  by  means 
of  cups  containing  mercury,  as  shown  in  the  figure,  or  by 
any  other  method. 

1029.  The  effect  is  surprising,  for  on  completing  the  cir- 
cuit with  a  piece  of  iron  an  inch  in  diameter,  in  the  proper 
form,  and  properly  wound,  a  man  will  find  it  difficult  to  pull 
off  the  armature  from  the  poles ;  but  on  displacing  one  of  the 
galvanic  poles,  the  attraction  ceases  instantly,  and  the  man, 
if  not  careful,  will  fall  backwards,  taking  the  armature  with 
him.     Magnets  have  been  constructed  in  this  manner,  which 
would  suspend  two  or  three  thousand  pounds. 

1030.  GALVANIC   BATTERY. — One   of   the   most    con- 
venient forms  of  a  galvanic  battery  for  the   experiments 
above  Described,  is  represented  by  fig.  255.     It  consists  of 
two  concentric   cylinders,  of  sheet  copper,  soldered  to  the 
same  bottom.     The  diameter  of  the  outer  cylinder  may  be 
six  inches,  and  the  inner  one  four  and  a  half  inches.      The 
height  may  be  a  foot  or  more.     Between  these  cylinders 
of  copper  is  placed  one  of  zinc,   but  so   as   not  to  touch 
them  nor  the  bottom.     This  is  best  done  by  tying  three  or 
four  pieces   of  pine  lengthwise  to  the  zinc  cylinder,  letting 
them  project  half  an  inch  below  the  bottom.      By  this  ar- 
rangement the  zinc  can  be  taken  from  the  acid,  or  plunged 


For  what  purpose  are  the  ends  of  the  wires  to  be  soldered  to  pieces 
of  copper  7 


340 


ELECTRO-MAGWETISM. 


Fig.  255. 


into  it,  at  any  moment.  Another 
cylinder  of  zinc  within  the 
smaller  one  of  copper  may  be 
added,  to  Increase  the  power, 
when  a  single  one  is  found  in- 
sufficient. This  must  have  a 
metallic  connection  with  the 
other  zinc  cylinder. 

1031.  The  cups  PN  are  the 
positive  and  negative  sides  of 
the  battery.      The  best  way  of 
forming  this  part  of  the  appara- 
tus is  to  solder  a  slip  of  tinned 
copper  to  the  inside  of  the  cop- 
per cylinder,  and  another  to  the 
zinc,   as   shown    in    the   plate. 
The   outer  ends  of  these  may 
readily  be  formed  into  cups  by 

cutting  the  copper  slip  one  third  in  two  on  each  side,  then 
turning  this  part  at  right  angles  with  the  other,  and  rolling 
what  were  the  outer  edges  together,  and  soldering  them. 

Such  a  battery  is  ample  for  all  the  experiments  we  have 
described. 

1032.  A  cheap  and  convenient  liquid  for  the  battery  con- 
sists of  water  saturated  with  common  salt,  with  a  little  sul- 
phuric acid,  say  an  ounce  or  two  to  a  quart. 

Describe  the  battery  fig.  255.    Which  is  the  positive,  and  which  the 
negative  metal  1 


j>C 
(S4C? 

£ 


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